Of course, this is extremely unlikely, and he might have a hard time getting in front of the right people to prove himself.
Pro sports doesn't have age limitations that I'm aware of; it's all entirely performance-related. People who can't perform don't get new contracts, regardless of their age, and of course as people get older (and accumulate more sports injuries), they become less competitive.
I don't think they wait for you to get injured. Before signing you on, they surely require you to pass some physical examinations first. Old people are unlikely to pass those psychicals regardless of how good they are at basketball, since their bones and joints are relatively weaker and therefore more susceptible to injury. What's the point of hiring the world's greatest basketball player if he'll break a hip the first time he falls? If a player has an unusually high risk of being severely injured, then it doesn't make sense to sign them in the first place. Doing so would be tragic and exploitative.
Anyway, the oldest NBA player ever was 45, and there have only ever been 7 who played past 42. Michael Jordan retired at 40 years and 58 days, and that was notably old. A player at 50 who makes the cut is basically fantasy.
Regular 50-year-olds, sure. But if they find some genetic mutant who looks like he's 25 even though he's 60, and passes all the physical tests as well as a 25-year-old, age isn't going to be a factor.
Meanwhile, over in the aviation field, that same genetic mutant would be unable to become a pilot purely because of his age.
Try to get a job in the NBA or any other sports team in your '40s and see what happens.