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a Bn size is the mean between An and An-1

The US doesn't "have to do things different" for the sake of doing things differently, as your words imply, nor is the sentence above about who uses what paper fully correct, either*.

The reason that the US (and Canada, most of Central America, Chile, and the Philippines) use different standard sizes* from Europe is probably pretty easy to figure out when you think about things like "there's a big fucking ocean between two of those places, but not between all of the countries in Europe."

The standard size of paper, according to the American Forest and Paper Association, comes from the days of manual paper-making, and their assertion that 44" is about the length of the average experienced vatsman's comfortable grasp. So a sheet is 1/4" that length. The US standardized its own paper according to what legacy equipment it had, and keeps those standards because even today, paper tends to not be shipped back and forth between Europe and the US unless it has to be, because paper and books are really fucking heavy, so why should either one of us change our standards? Doing so would require massive amounts of capital investment, and frankly, we like our paper sizes just fine. It's really not to our detriment at all. We don't really import a lot of paper, and in fact, we export a lot of it.

American paper sizes are also half of each previous size, it's just that our base is a rectangle, not a square, uses imperial measurements, and reaches back to measurements based on manual paper-making. Sure, we could spend billions of dollars changing our standards to meet that of countries that don't supply us with this good, creating a massive amount of industrial and consumer waste as everything from paper manufacturing mills and industrial printing presses to plastic binders and hole punches at schools all become garbage, but... why? We also use different standard sizes of snack food bags, based on how our industries developed, but there's no actual reason for those things to be standardized, so why, exactly, should they be? Because it bothers someone who doesn't use our machines and didn't know until today that it was different? That's not a real reason. That's just "haha the US sucks and is dumb and irrational."

No, it's actually super fucking rational when you remember that most European countries are smaller than US states, and we're standardized across the places where paper actually moves back and forth in massive bulk on a regular basis. You know: our own states, and Canada, and not Europe, on account of this being a huge fucking continent and paper being incredibly heavy and expensive to transport across oceans. That's why it's governed by the American National Standards Institute, which also governs or governed stuff like thread standards for nuts and bolts & exposure standards for film. The latter had the ANSI standard become the ISO standard, which is a great example of technology which was developed more recently and more specialized and thus not so deeply rooted and hard to change being much more possible to standardize.

tl;dr: all industrial standards like paper sizes have valid and long-argued reasons why they're like that, and unless you're coughing up the solution for changing something with hundreds of years of built-up infrastructure without breaking all of the industries that depend on that standard, the cash to do it, and the reason why all the old equipment that can't be converted should become garbage... fuck off, man, and leave us alone. There are real problems in the world, go solve those.