I don't think in most cases with major sports organizations that it's the players' unions demanding salary caps (they want minimums or floors for sure, but not maximums). Maybe that's what you meant when you said salary caps.
I mean, I don't know any pro athletes personally. You'd have to go ask NBA players what goes on behind closed doors within the NBPA.
From what I've heard from hockey (which is just rumors), the players definitely want maximum contracts and are hesitant when maximums are increased. This concern stems from Escrow, in which the yearly 'share' of the revenue for the players is estimated apriori. Part of the players pay is put into Escrow, and if the actual revenues fall short of the estimated revenues, then the players actually don't get their full contract money.
This is particularly problematic in hockey, where players sign long 8 year contracts. A megastar might sign a $10 million dollar AAV 8-year contract, but if the salary cap & maximum contract AAV rises 6 years later and teams overspend on free agents, they might actually end up losing some of that $10 million to Escrow recapture!
Thus, higher maximum salaries (or none) can seriously devalue long-term contracts. The shorter the contracts, the less the concern. This is why basketball has some of the highest salaries in pros sports (something like $50+ million now per year for supermax deals). Contracts are maxed at 5 years. In addition, most big stars get "player options" in their final year(s), in which they can "opt out" of their contracts. So if you're on a $30M AAV contract, and the salary cap rises dramatically with your $30M being slightly devalued, you exercise your player option to get out of that last year, and re-sign a new supermax deal.
For that reason, maximum salaries aren't nearly as big of an issue in basketball, and thus basketball has the highest maximum to minimum salary ratio.
https://www.cbc.ca/sports/hockey/nhl/escrow-players-nhl-labour-talks-1.5177705