There already exists regulations in place that do this.
In order to hire a mid-high tier reliever in the offseason, the Twins would have to pay about $10M to that player. The Dodgers or Mets, due their luxury tax situation would have to pay about $20M in order to acquire that same player, the player getting $10M and another $10M going to the rest of the players through the funding of their programs and remaining totals going to the rest of the league.
If a salary cap existed, there's friction league wide in those salaries, and that pitcher now might only get $7.5M.
So, tell me again, why are we trying to save the billionaires money?