Game theory tells us why it has to be mandatory: if everyone pays everyone profits, but for any one individual it pays off to stop paying as long as everyone else keeps paying (because they still receive roughly the same benefits). So most people stop paying, and everyone is worse off. It's basically the prisoner's dilemma.

Note how even denying non-payers all public services doesn't work. If you don't pay for the fire brigade but your neighbor does you profit (since a fire in his house is less likely to go out of control and jump over to your house). The resulting situation would be less fair than just forcing everyone to pay for firefighting services.

See my other discussion in this thread. I don't accept this "game theory" theory.