Why does Japan use the same type of AC power outlet as the US?

This answers primarily the first version of the question that is still evidenced in the misconception of the title, and thus the rest of this answer is still relevant to read in conjunction with semaphore's answer, which would otherwise re-inforce these misconceptions:

Q Why does Japan use the same type of AC power outlet as the US?

This is actually not the case.

Japan has not the same socket/plug system and therefore you will not find an argument for why they supposedly "adopted the US system." And neither for 'post WWII'. They only introduced a quite similar design after Edison screw plugs went out of popularity during the time-span before the war.

The US and Japan use different plugs – physically and electrically – and different standards to operate them. These differences may look small enough to group them into the same category of otherwise around the world much more different systems. But the fact that one could also stick a US blade into a Japanese socket doesn't make it a "same plug".

The Japanese plugs only look similar, but aren't fully compatible either. And it is all just historical contingency. Every country realised that the first de facto industry products that might have become any kind of 'standards' were horribly inefficient and unsafe. So they developed their own. And it took quite a long time to come to any kind of standard within any of most countries as the electrified.

Therefore the question starts from a false premise, and speculates on that: that there is deeper meaning in perceived identity when there is just similarity in pure chance developments and superficial morphollgical but untechnical categorisation…

This is clearly evidenced by early equipment not working or getting damaged if using the supposedly identical plug in the wrong region. The question would have made 'more sense' if it asked why these different plugs a grouped into the same category 'TypeA' when previously quite a lot of equipment would not work or get damaged trying to do so.

The reason why the world is now stuck with no less than 15 different styles of plugs and wall outlets, is because many countries preferred to develop a plug of their own, instead of adopting the US standard. In one sense those countries were actually right, though: the wobbly American plugs and their uninsulated prongs are almost prehistoric in terms of design and they are notoriously unsafe.

For decades, the International Electrotechnical Commission (IEC) tried to develop a universal domestic power plug, but time and again political and economic issues threw a spanner in the works. In 1986, the IEC finally presented the universal standard plug (type N) to the world, but unfortunately the initial enthusiasm had dampened. It wasn’t until 2007 that Brazil became the first country in the world to adopt type N as its standard wall outlet and plug top. The establishment of type N as the sole standard was motivated by the urge to sort out the motley collection of plugs in use throughout the country.

Many Latin-American, African and Asian countries are still in the same situation that Brazil used to be in. Standardizing on type N (or another safe and preferably widely used earthed plug system such as F, G or I, for that matter) is of course self-evident. But some countries just never learn. In 2006, Thailand deemed it necessary to develop a whole new power outlet system of its own, albeit compatible with type C, which is currently gradually being phased in. The mind boggles!

–– World Standards: "Why isn’t there a universal standard electric plug?"

And:

Even though the US and Japan both use plugs and outlets of type A and B they actually are not entirely the same. One of the two pins on US plugs is wider whereas in Japan both pins are the same width. This means that Japanese plugs can be used in the US, but US plugs often don't fit in Japanese outlets.

–– Japan electrical outlets & plugs

Because it is just a silly outcrop of stubborn insistence on perceived path dependencies:

Ok, maybe not every country, but with at least 12 different sockets in widespread use it sure as hell feels like it to anyone who's ever traveled. So why in the world, literally, are there so many? Funny story!

The more you look at the writhing orgy of plugs in the world, the sillier it seems.

I'd hesitate to refer to power sockets as a part of a country's culture, because they're plugs—they don't really mean anything. But in the sense that they're probably not going to change until they're forcefully replaced with something wildly new, it's kind of what they are

–– Giz Explains: Why Every Country Has a Different F#$%ing Plug

As Wikipedia explains

JIS C 8303, Class II unearthed[edit]

The Japanese plug and socket appear physically identical to NEMA 1-15. The Japanese system incorporates stricter dimensional requirements for the plug housing, different marking requirements, and mandatory testing and approval by METI or JIS.[49]

Older Japanese sockets and multi-plug adaptors are unpolarized – the slots in the sockets are the same size – and will accept only unpolarized plugs. Japanese plugs generally fit into most North American sockets without modification, but polarized North American plugs may require adaptors or replacement non-polarized plugs to connect to older Japanese sockets. In Japan the voltage is 100 V, and the frequency is either 50 Hz (East Japan) or 60 Hz (West Japan) depending on whether the customer is located on the Osaka or Tokyo grid.[50][51] Therefore, some North American devices which can be physically plugged into Japanese sockets may not function properly.

It is just the very basic form that allows for a superficial similarity and half-way easy compatibility, often with adapters or 'electrical logic' required

The superficial similarity is the "Type A" form. That does not mean they are identical, just similar.

The Japanese JIS specification is different from the American one, not only in voltage, as Japanese Wikipedia illustrates:

type    Plug standard   Voltage (V) Allowable current (A)   Grounding electrode polarity    fuse
A       NEMA 1-15   no polarity     125       15    None    None    None
        NEMA 1-15   with polarity   125       15    None    Yes None
        JIS C 8303  Class II        100       15    None    None    None
B       NEMA 5-15                   125       15    Yes Yes None
        NEMA 5-20                   125       20    Yes Yes None
        JIS C 8303  Class I         100       15    Yes Yes None

For the differences:

Generally speaking, most hair dryers, curling irons, hair straighteners / flat irons and other bathroom appliances from the US and Canada will operate on 100 volt Japanese electricity, albeit less effectively (for example, the heating element won't get as hot) but it'll work, and you won't start a fire or anything. You'll need an EA6 adapter to allow the appliance to plug into the Japanese Type A wall outlet.

Other conventional appliances which are not multi-voltage compatible would require a Japan/US "booster" transformer (to change the voltage from 100 volts at the outlet to 120 volts at the plug) with a wattage capacity that is sufficient to support the wattage requirement of the appliance.

Japan is the only country on the planet where the electrical systems supply 100 volts of electricity, as opposed to 120 volts in North America and 230 volts in most of the rest of the world. Most North American appliances have a voltage tolerance of roughly +/-10%, though some equipment is more sensitive, and may have a tolerance more along the lines of 5% or even 3%. In any case, 100 volts is slightly outside the range of tolerance of most appliances. How big a deal is it? Well, it depends on the appliance, and how it's being used.

Make no mistake, even a slight undervoltage condition is not at all ideal, and not good for the health of an appliance. But undervoltage is generally considered less serious than overvoltage. You're not going to "fry" your appliance, and it's not going to catch fire or anything. In fact, it'll probably work, though less-effectively, and electronics may "act weird." And over time, undervoltage absolutely will damage and eventually destroy an appliance. That's why US/Japan "booster" transformers exist. Manufacturers wouldn't produce them if there wasn't a need for them.

If you're bringing North American appliances to Japan for an extended stay, or a permanent move, you'll want to use a booster transformer to change the voltage from 100 volts at the outlet to 120 volts at the appliance's plug, the voltage the appliance was built for. And if the appliance is particularly sensitive, or if the appliance "acting weird" is unacceptable (think medical equipment) then you need to make sure it's getting the voltage it requires. On the other hand, if you're just going for let's say a week, and you don't mind if your hair dryer doesn't get quite as hot while you're there, then you probably don't need to worry about it too much.

The electric frequency is different on either side of the Fujigawa River in Shizuoka Prefecture and Itoigawa City in Niigata Prefecture, with 50Hz in the east (Tokyo, Yokohama, Tohoku, Hokkaido) and 60Hz in the west (Nagoya, Osaka, Kyoto, Hiroshima, Shikoku, Kyushu.) Does it matter? Again, it depends on the appliance. Some appliances can handle either frequency, and for others it's not really a significant factor. Motors built for 60Hz will rotate more slowly on 50Hz, and will heat up more quickly (and over long periods of time will eventually burn out) and digital clocks and timers won't keep accurate time, they'll "run slow." Don't bother bringing an alarm clock that's not compatible with 50Hz, overnight it'll "lose" more than a full hour! But it's not going to affect your phone, tablet or laptop. And it's probably not going to be a big deal for a hair dryer for 10 minutes or so at a time.

But, again, anything that's going over there for an extended period of time, or permanently, really needs to have the voltage and frequency it was built for. And if it's a particularly sensitive piece of equipment, or something incredibly important like a piece of medical equipment that absolutely must work precisely as it's intended to, it needs to have the correct voltage. Don't chance it, give it 120 volts by way of a US/Japan booster transformer.

Japanese Wall Outlet Variance NOW, ABOUT THOSE WALL OUTLETS

Image 1 (top-left) is a typical US / Canadian wall outlet just like the ones in your home. It's both grounded and polarized.

Grounded refers to the presence of the third, round pin in addition to the two vertical blades. Polarization refers to the left vertical blade being taller than the one on the right.

All US and Canadian wall outlets are required to be both grounded and polarized, but plugs aren't. Some plugs have the round pin while others don't, and some plugs' vertical blades are the same height while others aren't. You're probably used to that. But since the outlets are all grounded and polarized, it doesn't matter what the plug is like. They'll be able to plug into the outlet regardless.

But in Japan, virtually all outlets are non-grounded. Image 2 shows a Japanese outlet which is polarized (the left blade is taller than the right) but not grounded (there's no receptacle for the round grounding pin.) So then, what if your plug has that third, round pin? You can't plug into the non-grounded outlet. Image 3 shows a Japanese outlet that's neither grounded nor polarized. In that case, even if your plug doesn't have the third, round pin, it still can't plug in if the plug's blades aren't the same height. Most Japanese outlets are like image 2, non-grounded but polarized. But non-polarized outlets like image 3 are pretty common, especially in older buildings.

Your phone charger's plug almost certainly has just the two vertical blades, and those two blades are probably exactly the same. In that case, you're good to go, no worries. But your laptop's plug is probably polarized, with the left blade being taller. In that case, you're good to go if the outlet is like image 2, but out of luck if the outlet is like image 3. And your hair dryer's plug probably has the third, round grounding pin. In which case, you're out of luck entirely.

Fortunately, we have plug adapters for that. Our item #EA6 is neither grounded nor polarized, therefore allowing you to plug into any kind of wall outlet you might encounter in any given building in Japan, regardless of what your plug is like.

The above list goes on for quite a bit.

If words are too complicated to understand, perhaps it gets easier to see the difference if using pictures?

Japanese plug system from Wikipedia Japanese:

US plug system from Wikipedia:

If appliances get designed intelligently to accept and work with 100–240V and 50–60Hz etc, and thus work, with adapters, that does not mean the plug system is the same! It means nothing more but manufacturers accounting for the inherent differences to expect on a an interconnected global market.

When the different plugs within the 'same' type category were introduced you could try to plug those things from the US in Japan: that would perhaps not work at all, work badly for you, your appliance or overload the Japanese wires.

Why is the Switzerland socket different from all surrounding countries in Europe but has the exact same type as Rwanda? These actually are the very same standard! One might interpret quite a few things into that. But that probably doesn't mean one gets especially useful information out of it? If systems aren't technically the same but just look similar any connection and suspected deeper meaning is ever more absent.

For how the plugs evolved:

Edison’s plants provided light to Wall Street, New York City, and London. Edison had thought of a number of applications for this power, including a system for household wiring that used the existing piping of the house as its framework. However, there was no convenient way of tapping into this power for anything other than lighting. Amateur inventors came up with a number of appliances that had to be directly wired to the household system, including Harvey Hubbell, who designed a “Separable Attachment Plug” that connected directly into a light socket. This plug had to be wired to the appliance, but the user would not have to deal with live wires connected to the house. He then improved upon his own design by making the plug itself able to separate: one portion of the plug could be left in the socket, while the other was a two-prong plug that could be separated from the socket plug.

After Hubbell’s innovative plug, the next advancement came from a man named Philip F. Labre in 1928. In order to reduce electrical shock as a result of a short circuit (an undesirable connection), he added a third ground prong to the plug to be inserted into a third hole in the socket. When a person unknowingly creates a short in a circuit with an electrical plug, his body becomes the only path from the live wire of the plug to the ground. Labre added the third prong as an alternative “path of least resistance” to bypass the person. This means that instead of flowing through you, the electrons flow through the ground prong to the earth. 4. Labre’s outlet is the model for the modern outlet. Aside from the ground prong, there are two prongs that connect to the live and neutral wires. The live wire carries current into the appliance, while the neutral wire carries current back to the electric panel, completing the circuit [4:3]. Without the grounding, Labre’s outlet would be called “unpolarized” because the two identical prongs of the plug may be inserted into the outlet in one of two ways. A “polarized” outlet allows the plug to be oriented in only one way (“Household Wiring”). Worldwide, some plugs have different-sized prongs (like in the US), some are set at different angles (like in some European countries), and some can have completely different shapes (like in Japan). –– Robin Hartman: "A Powerful History: The Modern Electrical Outlet", Illumin Electrical Engineering, Issue II, Lifestyle, Volume X, June 19th, 2008.

Another overview is presented by the Plug-Socket museum: US plugs and sockets - origin and early models and especially since "Also Japan uses flat blade plugs and sockets, in part comparable to NEMA types; they are shown on a separate page. " Japan – overview of types of plugs and sockets:

Japan uses flat blade plugs and sockets according to Japanese JIS 8303 standard. The 15 and 20 Amp types are similar to U.S. NEMA configurations. …

Japan follows the North American pattern flat blade configurations for 15A-125V (left), 20A-125V (middle) plugs. The Japanese 20A-125V without earth connection (right) has an unique shape for the neutral (W) pin. …

Socket (13) and plug (14) rated at 15A - 125V with a U.S.-style twist lock mechanism. However these Japanese models are incompatible to NEMA L5-15 plugs and sockets. Japanese plugs have a slightly different pin position and the earth pin does not have a hook.

A Japanese site explains it thusly:

Different countries have different standard voltages and electrical sockets. Some of the gadgets and devices we have may not work in some countries if the voltage, plugs, and sockets are not compatible.

The U.S. developed the power delivery system along with the modern electric plug. Other countries did not find the U.S. standards (60 Hz, 110 V and their plug system) as efficient for the power supply being utilized.

Each country began improving on what they thought would be the best way to deliver electricity that is safe and customized to their standards. This resulted in different countries having different plugs and sockets.

KPC International: ELECTRIC SOCKETS AND VOLTAGE GUIDE WHEN IN JAPAN

Since these original designs and their variations or improvements around the world date to the 1920s and 1930s, with further developments on that front hampered by another front – it follows that at the time of adoption Japanese did not receive any post-war aid but decided that absent a whole domestic 'invented here' solution some parts of the US design that became standard in the US after the Edison screw finally disappeared for appliances other than light in 1931 was 'good enough', other aspects not, and thus these were changed.

In case of Japan again: the literally first search engine hit for pre war Japanese radio,

_{Tokushima Radio Promotion Association Special Type A Receiver; Hayakawa Metal Research Institute Co., Ltd. (around 1936)}

青年団4号A型受信機　(放送協会認定第11045号)　山中電機(株)　1937年 　　　

　取説表紙(個人蔵)、裏表紙には山中電機株式会社特製とある。　　回路図　(取説より) TUBES, 24B-24B-47B-12B/F, Magnetic Speaker

山中電機の放送協会認定品、M-48型をベースとする青年団向け高一セットである。デザインの基本はM-48型と同じだが、スピーカのグリルが「青年」の文字を図案化したものになっている。他社の青年団受信機も認定品をベースとし、グリルに「青年」の文字を図案化したものを使っている点は共通する。高一であるのは、電波の弱い農村部向けであったからだろう。

本機のツマミはオリジナルではない。 (所蔵No.11306)

Finally, a little explanation for the path dependency baggage concerning frequency as the Japanese explain it delightfully easy to kids:

In the Meiji period, 50Hz (Hertz) generators were imported from Germany in the Kanto region, and 60Hz (Hertz) generators were imported from the United States to the Kansai region. And there are two frequencies.

Some household electrical appliances that use motors, transformers, and electronic timers with built-in equipment are based on this frequency, so moving parts between the 50Hz and 60Hz areas requires replacement of parts and adjustment of equipment. There are cases.

Precautions when using electrical products overseas Some things can't be used overseas Japan's voltage is 100V and 200V, and overseas is 110V, 120V or 220, 240V. If the voltage is different, the electrical product may break.

When used in a different location, the electricity is flowing to properly check or the electrical outlet display confirmation trying.

There are various outlets.
If the frequency varies from country to country, the voltage and the shape of the outlet will also vary. Unless it is an electrical product that says it can be used anywhere overseas, there is not much you can use Japanese products as they are.

When you go abroad, there are small capacity transformers that adjust the voltage and plug adapters that match the shape of the outlet at travel goods dealers and rental stores.