If checked baggage / luggage size limit is 62-inch. Isn't most luggage sets oversized?

Most airlines just aren’t that strict. I’ve flown a handful of times with bags approaching or slightly exceeding the maximum linear measurement but nobody has ever measured the bag. Manufacturers have an incentive to push the edge of the envelope so as to be able to make bags with greater internal capacity.

Of course, some airlines are strict, notably low-cost carriers, and I’ve never flown with one of these bags on such an airline. But even still, they tend to be strict with weight and with the dimensions of carry-on bags, which are easy to check because they specifying maximum values for each of the three dimensions and check the bags against these by seeing whether they fit inside a box.

Measuring three dimensions separately requires a ruler or measuring tape and is subject to error and disagreement. Being picky about bags that are close to the limit is likely to cost the airline more than it collects in oversized baggage fees, most tangibly in employees’ time, but also in intangible ways such as ill will, customer dissatisfaction, and lost business.

Nowhere does it say that you need to take every bag from your set with you, or that the airlines should be mandated to allow any arbitrarily large set of luggage that some manufacturer may design and sell.

If the latter were the case I’m sure there’d be plenty of leather working shops who’d churn out custom sets with total sizes larger than the cargo hold of a commercial airliner, just so someone can use them as a kludge to sue an airline (likely an American one) for billions in compensation for ‘not being allowed to take my matched luggage’.

It is your duty as a passenger to select your luggage based on the maximum size AND WEIGHT restrictions imposed on you by your carrier(s). And do keep in mind that if you change planes during your journey you may encounter the situation where one flight has a smaller luggage allowance than another, the smallest will now effectively apply to the entire journey.

Of course you can always pay to have (some of) your luggage shipped through other means.

Airlines having their own specific luggage size retrictions doesn’t mean that luggage makers should abide by them for every suitcase or bag in a travel set; after all, it’s a travel set, not an airline travel set. Lots of people travel by train / car / ship / bus, which have more relaxed luggage size rules than airlines (if any at all), so there’s no reason for luggage makers not to make bigger suitcases for those who need them.

Also, airlines are known to change their luggage size requirements, so there are "airline approved" travel sets out there that were approved but now they are not anymore.

This way of measuring is called linear inches and you are right that most checked luggage limits are specified in terms of linear inches while the majority of carry-on luggage is specified by maximum size along 3 dimensions, mostly because storage is much more constraint in the airplane cabin.

There are certainly luggage that is oversize which people are allowed to use by paying an oversize surcharge but most 3-piece luggage sets sold are generally sold with the largest suitcase close yet under the 62" limit as it is very common. It might depend where you shop but I have personally bought multiple sets over decades and never had to look particularly long to find a suitable size. Typically, the 20-24-28 combination allows the 3 pieces to fit nicely together. I once bought a 26 single-model which is a great travel size but didn’t fit in the 28", later I got a 31" model which still was not oversize as it has only two wheels on the side of the suitcase.

The size of the 28" suitcase from the latest 3-piece set that I bought measures 29.5 x 20.5 x 11¾" for a total just under 62" and it most others tend to lineup with that number. The largest in this set if 60" and this expandable set comes with a suitcase that is 61" normally and expands to 63" to allow the oversize option if needed. It seems it could be just a matter of sampling but it really looks like suitcase makers know the limit and try to get right up to it. You will notice that due to common weight limits for checked luggage, it is hard to fill an oversize suitcase and not be over the weight limit.