Different leagues and different rules but in the MLS the league owns the clubs as well as the players so there is no third party involved. The owners each put money into individual franchises, including the franchise players, and control some of the ancillary income. All the revenue gained by the league is distributed among the franchises.
In England the clubs are independent (private or public). The problem with 3rd parties is that the league thinks that it reduces competitiveness. e.g. if West Ham only pay 50% of Tevez fee it is unfair to the other clubs like Charlton, Watford etc. who paying full price for players.