If this was the only reason to have a union, you would only expect unions to exist in sports leagues that have a monopoly. Yet that isn't what we see in practice. The WNBA and the MLS both have unions. The NBA G League is moving to form a union as we speak. These are all leagues that face stiff competition from abroad and it is common for American athletes to go play in those foreign leagues. However that competition between employers isn't enough to give the athletes the negotiating power that they can command with a union.