Why do (almost) all countries have a flag, coat of arms, anthem, national holiday etc.?

The most base answer would be: Humans naturally like to conform.

More specifically, if you want to participate in the current world order, it's in your interest to go with what's currently in vogue.

One example is Russia. After the fall of communism, Russia adopted an anthem without lyrics, and it proved to be very problematic. Why? because during sporting events and the like, people sing their anthems. An unsingable anthem stands out as strange and it affected the athletes' morale.

Another example is Imperial China. There was no flag for Qing China, but they were forced to make at least a naval flag, because according to maritime law, ships without an official naval flag were always under suspicion of piracy. Chinese ships thus had to resort to flying the naval flags of other countries, which, as you can imagine, is a pretty big loss of pride. The Arrow Incident also partially arose because the Chinese ship sent to arrest British Sailors accused of beating merchants had no standard, so Britain claimed they didn't know it was a military ship carrying out an official duty - (as opposed to say, a pirate raid). It's an excuse, but the Qing court realized that they couldn't do without a naval flag, which is why the Yellow Dragon Banner was made.

As for national day, well, if you have a birthday, why shouldn't your country have a national day? It has to have started at some time.

While Europe and the US originated most of these practices, it also bears to note that Europe and the US also had the lion's share of world power at that time, and it's in your interest to do as what they do.

Now if you think about the full process of an awards ceremony at the Olympics - you wear a uniform, which probably means you'll need some kind of crest on it to identify that yes, this is your guy and not your mortal enemy neighbor's. You go up the podium and they raise your nation's flag and play your anthem. So what if you don't have one? Your country will probably break their work flow and look like an a**, and your athletes will probably be embarrassed that they had to stand out like this.

Same with something like an international summit. They'll usually fly every country's flag there at prominent places, but you don't have one, so now nobody knows you're important enough to be there.

Making a flag/crest and writing an anthem is, quite frankly, on the grand scheme of things too much trouble not to have for a country if it chooses to have any presence in the current world, so every country has one and they're all following about the same format.

It is not exactly true that each nation has one national flag.

Famed vexilogist (flag researcher) Dr. Whitney Smith divided the uses of a national flag into six subcategories. Flags used on land and ensigns used at sea, and three categories for each: national (used by ordinary civilians), state (used by the government) and war (used by the military - and often distinct from military colors and standards). Many nations thus have two or more different national flags. I believe that the United Kingdom has as many as five different flag designs for the six subcategories of a national flag.

Similarly in the 19th century many monarchies had different royal coats of arms: the greater arms, the middle arms,and the lesser arms.

The reason why most nations have official coats of arms is because they are used on their great seals.

Seals are used to authenticate documents. The design of great seals for national governments used by European nations and most of their former colonies is circular, with the national achievement of arms in the center and a circular border with an identifying inscription. Thus most nations have national coats of arms or somewhat similar looking national emblems, to put on their great seals.

And of course a national government has a lot of different departments and local offices and services and agencies, and each usually has its own seal that is usually similar to but not identical with the great seal. thus every modern nation is full of government entities with their emblems (for use on seals) that are often coats of arms.

These national symbols are not quite as universal as you seem to imagine, though they are indeed widespread. And where these symbols do exist, they are given widely different degrees of importance by those countries.

National holidays and national anthems are definitely not one-to-a-country as you claim, though for convenience they are often treated this way. For example, the United States has Independence Day, Thanksgiving, Memorial Day, Labor Day, and Veteran's Day, all of which can be considered major national holidays. The fact that one of them (Independence Day) is branded as "the national day" means very little in reality. Some countries similarly have more than one national anthem (e.g.: Scotland), or a national anthem that is distinct from their royal anthem (e.g.: Sweden).

As for national flags and coats of arms, these do show something closer to a universal one-to-a-nation standard, though there are plenty of examples of nations with both lesser and greater forms of their coats of arms (e.g.: Sweden), and many nations fly different national flags on land and on ships.

Furthermore, not every nation has a "coat of arms", though many nations have a "national seal", "national emblem", or similar device that performs a related function. Some nations have more than one of these.

Other answers highlighted the fact that all this is not as universal as your question suggests but I think you are nonetheless getting at something important.

The modern state is something quite new and “localised” historically. It appeared in Europe in the 17th and 18th century and is often linked with the 1648 Peace of Westphalia. National anthems or national days were often promoted later but the Westphalian system is still to a large extent a cornerstone of international law. This means that to be recognised as a state, a country will usually emulate the European model, assert its sovereignty over a specific territory, become a member of the UN, etc.

And that's exactly what many countries in Africa, Asia or elsewhere have done through several waves of colonisation and subsequent independence. With a few exceptions (countries like Guinea, Congo/Zaire, Algeria or Libya come to mind), the newly formed states took over the European model wholesale just as they gained their freedom from the former colonial power.

Now, national anthems and holidays are mostly for internal use and not strictly necessary but (nearly?) every country in the world (and many unrecognised would-be countries) has a flag. It's a simple detail but there is no reason why it should be that way a priori, save for the influence of the European notion of what a state is and the desire of the local elites for their countries to be acknowledged by the rest of the world as such a state.

Incidentally, many conflicts can be interpreted in part as a result of attempts at forcing this nation-state model on societies that previously knew different governance structures.

And if you are wondering how a different approach could look like, consider Daesh. Not only are they attacking many things the rest of the world regards as basic rights or values, they also reject the international order entirely. They are not trying to take over a country (be it Iraq or Syria) for a particular group or ideology or to have their power on this territory acknowledged by everybody else – like the Islamic revolution did in Iran for example – they purport to create something radically different, outside of the current international system.

To be pedantic, and to repeat some of what's already been said in comments ... there isn't, in fact, absolute uniformity in the way those national symbols have been constituted around the world.

The Gaddafi-era Libyan flag was something of a non-flag, an idiosyncratic statement. Arguably the Saudi flag is as much a banner as a flag. The Nepali flag, as you say, is more of a pennant than a flag.

And at least two countries don't have a national day, according to this Washington Post map.

As for national anthems, some countries share the same tune and, as far as I'm aware, at least one country (Spain) has a national anthem with no words. So it isn't as if there are any basic rules on anthems (words, uniqueness) which the world's states have signed up to.

But in any case, if you're establishing a new sovereign state, and even if you've already got a cute ceremonial rod or a damn fine national dance, why not also find yourself a flag, and a tune and a feast day? They cost nothing, add to the gaiety of nations, and the neighbours, even if they aren't going to force you, sort of expect you to have one.