Generally "the commons" only exist if there is no one capable of policeing them.
The tragedy of the commons is an illustrative example of what happens when there are no property rights, with a disinterested police and judiciary to enforce them. On a realistic basis, there can be no true "global policeman" without a true "global judiciary"; given the hijacking of international institutions to promote various schemes (generally anti-western), maybe a "global posse" might be a better description of the state of affairs. Yes, the US is the Sherrif and the Judge, but would you really want to submit to the rule of an organization that until recently had Lybia leading the Human Rights comission?
The United States has several interests in being the global posse;
Freedom of the seas for American trade
Freedom of the seas for allied trade
providing a low cost alternative for allies and neutrals for freedom of the seas and providing reasons for them not to spend money on building their own, potentially competative sea power.