I don’t think this is fully correct. Athletic skill is not universal across sports. A athlete that can be trained to be a star football player may not be able to be trained to be a star baseball player.
I think there is a more self selection process happening for athletes and sports. People with natural athletic inclinations try lots of sports young, they will do well in the ones they are most suited for, and begin taking that seriously.
I don't think this means as much as you're putting weight into.
I think the fact that somebody like MJ or Tim Tebow could even get a try-out in a different profession sports really speaks to top level talent being fungible. Like just imagine somebody practices being a Doctor for 20+ years and then gets an interview to be a World Cup Referee. Sure, they might not succeed at the other sport but the fact they can still do it is I think proof of sports fungibility.
https://en.wikipedia.org/wiki/List_of_multi-sport_athletes
The list for college and high school would be huge. There is such a thing as athletic skill, I’ve heard it called a kinesthetic gift. People with particularly good builds, strengths, speed, agility, etc. can train those attributes across several different disciplines. As you get higher and more elite you will eventually have to specialize. “Jocks” in high school frequently played multiple sports and many lettered in multiple as well.
There's kind of a soft cap on NFL player height at about 6'5" or 6'6" - hardly anybody is taller than that. But the NBA is majority guys 6'6" or taller. That split isn't because all those kids got sorted into the right sport when they were kids. It's because if you're enough of an athlete to go pro and tall enough to make a living off basketball, that's a lot easier life with a longer career than playing football.