My argument would be that heterogeneity among playing talent is at least part of the answer. Differing talents leads to differing earning potential which results in a disincentive to form a cooperative structure since those players with the greatest earning potential will wish to be able to transfer between teams easily to maximise competition for their services. Martin Ricketts explains the problem as
Further, to minimise antagonism a rough equality in the division of the residual will be necessary and this may conflict with outside opportunities. Those with high transfer earnings reflecting high productivity elsewhere will desert the co-operative. It is for these reasons that control of the firm by its labour force is usually found in circumstances which permit a high degree of common interest.A cooperative form of organisation would hinder rapid transfers between clubs. Issues that could slow transfers could arise if, for example, the terms of the exit have to be negotiated with the remaining player/owners of the cooperative team. The remaining player/owners could, as an example, be unable or unwilling to buy out the exiting player or any of them could veto an incoming replacement player/owner. Transfers would be easier if the player was just an employee of the team rather than an employee/owner.
In addition there are principal-agent problems such as those which could arise between the manager or coach of the team and the player/owners in their roles as players and as owners. Who is the principal and who is the agent?
I don't know of any player owned teams - if anyone does have an example please give it in the comments - and heterogeneity of human capital is part of the reason why.