Yeah, I’ve used a sheet of paper as a ruler too...
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.
There is also a C series of sizes which are slightly larger than the A sizes and therefore useful as envelope sizes.
The creators of metric weren't above buggering it to fit human scale needs.
Take the length/weight relationship.
Definitionally, it'd be way more elegant for the unit of mass to be based on the unit of length directly, a cubic meter of something, but having your base unit of mass be a ton wasn't going to fly.
So they instead tried for 1/100th of the meter and landed on the gram, but it turns out they misjudged and now your standard unit of weight is the prefixed kilogram instead, because everyone used kilograms instead.
Which is to say, if you didn't get a pretty good paper size out of the definition used for A0, someone would have found a different definition which did produce a pretty good paper size, and then declare it was the only natural one.