The only sport that matters, football, has no salary cap whatsoever
But as for the ones that do have a cap, I suppose the sport execs find a way to make sure the most talented players end up receiving much more than their salary. How much does Lebron James get out of marketing contracts? I bet it's much more than your average NBA player. That meas in effect there is no cap. So while the cap may boost competition between the teams, they do nothing to enforce equality of wages among players.
Yeah and that's why football is so uneven and boring with the same teams winning year-in-year-out.
The thing with American sports is that nobody else plays them, so the top atheletes can't really go overseas and make more money elsewhere. There's a monopsony market there. The same thing is true of Australian Rules Football, which is a sport unique to this country. Rugby League and Rugby Union are actually interesting, because players
can move overseas, and some do, particularly with Rugby League players heading to Europe.
Sports with a salary cap also typically tightly control player recruitment, either through a draft system or through feeder leagues and zones. Players can't just be recruited willy-nilly, there are binding contracts and league rules about movements. The AFL has a trade window where players can only be traded between clubs for 2 weeks at the end of each year. Some leagues actually make an exception, allowing one or two "franchise players" to be paid an unlimited sum outside the cap. The NFL in the US does this, and Australian soccer's A-League uses it to attract international talent (or our own stars who currently play elsewhere).
The point of the salary cap is to equalise the ability of teams to obtain talent, making sure that teams compete solely on their ability to make good draft picks and recruitment decisions and to innovate in tactics and training. So individuals having the ability to get external contracts based on their own star power is actually fairly independent of that, since LeBron can make that marketing money at any club.
And, additionally, most leagues actually regulate third-party arrangements quite tightly, because of the capacity for abuse. In the case of Australian Football, we've seen players given part-time jobs with club sponsors (my team the Sydney Swans have a policy that all players should work or study one day a week. Some players sutdy, one guy with a finance degree now works at Citi, etc), but the AFL actually investigates and scrutinises each individual deal for whether it was used in attracting or retaining players at the club.
My guess is that if football were to ever go mad and impose a salary cap, it would be an agreement by the biggest clubs in Europe to limit their spending on wages to some extremely high ceiling (say, half a billion euro). The purpose wouldn't be equality, but to prevent a spiraling arms race whilst ensuring that Barcelona can still out-spend Zaragoza and Manchester United can still outspend QPR. Still not likely, of course.
(Yes I am a nerd for sports administration too)