Its a very one sided scenario at the moment. I've often thought that a restraint of trade clause is necessary, allowing clubs to control the transfer of players to a greater degree. At the moment players can do whatever they want regardless of legal contracts, restraint of trade preventing them moving to a club in the UK wouldn't seem particularly onerous or illegal. If both parties agree to a move then the clause could be removed but the club would be in the driving seat as opposed to being powerless. I'm sure it been discussed at length somewhere but never looked for it.
There are lots of examples, both in sport and elsewhere, of the “bastion of capitalism” regulating markets where it is in the public interest to do so. Modern Britain and Europe is in many ways more wedded to the doctrine of the free market than the USA - parts of it anyway.
Definitely football, which is an unregulated free for all in Europe, and clearly less so in the US. I thought that was your point?