Of all the obfuscation and misdirection surrounding MLS’s allocation rules, perhaps the least confusing is the actual breakdown of transfer fee money.
As a baseline, MLS owns every player contract. The league operates in theory like every other league in the world, where the individual clubs hold the entirety of the contract in their own hands. Clubs negotiate with players, clubs sign players. In MLS, clubs do the legwork (or most of it anyway) and the league office has final say, a relic of an era when the league’s clubs could not be trusted financially to uphold the burden. Whether or not those days are entirely kaput (they probably are), the structure persists. And I imagine it’s an incredibly difficult thing to dismantle.
Of course, the league rarely throws up roadblocks to player sales and signings. It can, technically, block any signing and refuse any incoming transfer offer. But it would be prohibitively problematic to do so, and the rancor caused among the front office it denied would be too toxic to consider it anything approaching a normal practice.