As regards metric/A* paper sizes, it seems like just a coincidence that this scheme resulted in a standard size that is useful for everyday documents, since it only works for powers of 2 and starts with the definition of 1 square meter. If a meter were 1.5x smaller or larger, then I don’t think there would be a standard size that works so well.
EDIT: Being curious about this, I did some more reading, and discovered there is a “B” series of paper sizes that maintain the same ratio relationship, but are exactly in between all the A sizes! That’s useful.