Capitalism (or rather 'free' in the technical sense markets) solve a coordination problem. They don't solve the tragedy of the commons (unless you start paying people not to polute the commons, but that is very perverse).

They are by far our best bet at solving large coordination problems through price signals. Even though they are far from perfect. I do believe that free markets require capitalism (i.e. profits go to the owner of the capital rather than those who do the labour). But nothing there is against strong regulation, collective bargaining, and anti-trust. Nor is there anything about companies being soley beholden to their shareholders.

Also, 'free' markets can only exist with a whole bunch of regulation, and even then some markets (e.g. emergency care) can never be free.