That sounds like a case of "Tragedy of the Commons", which is not free market.

Also, police is a requirement because libertarianism relies on government to protect peoples' rights. Gutting the police department is what anarchists do, not libertarians.

If you want to know of a successful libertarian experiement, see the founding of the United States. (Excluding the slave states, of course. Slavery is antiethical to libertarianism.)

No true scotsman

You mean the Articles of Confederation that failed because the government wasn’t strong enough?