That actually sounds like it could work if the next CBA could include it. You'd still have the risk that players would group together to form a Miami / GSW superteam, but in theory every team could have a superstar.
It wouldn't even need to be unlimited, for someone like LeBron winning is probably more important than doubling his salary. But if say Dallas could offer $10m more a year to a Chris Paul than another team who already has a star, and still have the cap space to build a team around him, then that could encourage competition.