It’s not that there is a relation, it’s that it’s simple. If you put 288/187 inch of water on a standard letter paper, you get exactly one cubic foot of water, but I wouldn’t say “The fact that a cubic foot of water has a relation with the size of the paper we use is just poetry”.

It also is a happy coincidence that the idea “if we cut a page in half, the two parts should have the same proportions” leads to usable paper sizes. If it weren’t, we wouldn’t have this system.

And has this ever been tried for 3D, say in storage boxes? The proportions of a box would be about 1 : 5/4 : 25/16. That’s a bit cube-ish, but doesn’t look unusable to me.