Given powder advances I wonder how much shorter all these cases could be if designed today. When I first started reloading almost 40 years ago I was shocked how little room the powder took up in a .38 special case. I reloaded some 44 specials yesterday (the last of my large primers) and the powder is way down there in the case.
45GAP is the answer to that I think, although to be fair it has a modern MAP to go along with its shorter case length. 9 to 38 is along the same lines when you just look at it topically like that. Shorter, modern MAP, and 38 is now about the size of a 9mm casing. The heavy 9mm 15xish grain 9mm bullets give some data for playing with.
On the 10mm, I'd put my money on the 30Rem casing theory. That is what it was when handed to the original manufacturing team and they ran with it because they had no data or push to the contrary.
I doubt it is case volume or powder charge weight. The 357Mag is lighting off charges of 10gr of Blue Dot, 10gr of Power Pistol, and even 15gr of 2400 with non-magnum primers. Those are similar to 10mm charges so, clearly you dont need the stronger large primer to light off those weights. I dont have Quickloads up but I bet the case volume with 200gr bullets is decently close, might be wrong though.
I'm betting on tradition and lack of engineering need.