Rather than quote 3 posts, I’ll just quote one.
The belt, up to a certain point, is supposed to be indicative of skill. And other things as well. When you get up there in rank (and usually age), you’ve proven your skill. From some point on that’s different for every school, rank is about your contribution to the art rather than your own skill. Get up to, say 7th dan and it’s all about spreading the art and advancing it one way or another. And promotions are based on that rather than who you can beat up.
Kids’ ranks transitioning into adult ranks are handled very well in my organization IMO. The curricula don’t match up; junior black belts are somewhere between 3rd and 2nd kyu adult syllabus. Kids’ belts have the white stripe going the length of the belt. When a kid becomes adult age, they wear the kid belt and are taught as adults. They wear the kid belt until they earn the comparable adult belt like any other adult would. Junior black belts do the same, but they test for adult black belt like every other adult when they’re ready.
I’ve seen my CI test kids for the comparable adult belt and simply promote them to it during class. It depends on several variables and I completely agreed every time. It’s usually dependent on the kid and the timing.