I always thought it was strange that James would want 23. I'd get it growing up, but when you are anointed the next great thing, why would you copy that from the previous one?
Probably has more to do with that being the number they've had all of their lives. When a kid shows himself to be as good as guys like Lebron and AD, the coach will usually give them their pick of numbers first.
As kids they pick it because it was MJ's or whoever's number. Then, by the time they get to the pro's, they think of it as their number.