Their talent is their leverage. Some players get paid $100m+ for their talent.
Athletes' unions exist to protect the players at the bottom, who are just talented enough to play at the professional level but aren't superstars, like the offensive line in football or the bench players in basketball.
Notably: many of the athletes' unions predate the era of the monopolistic sports leagues. (The modern NFL, MLB, and NBA are all the products of the mergers of smaller leagues, and their players' unions formed before they achieved monopoly status.)
