I believe the government should be abolished, and the free market should replace its usual functions.
That all depends on circumstances. If we just removed the government spontaneously, then yeah, someone would form a new one, and the U.S. (or wherever it is) just gets partitioned.
Our strategy depends on not just overthrowing the government, but making it next to impossible for a new one to happen. Sadly, this can't occur overnight, because there are two things that need to be done.
First, enforcing taxation can't be profitable, and it must result in a significant loss on the state's part.
Second, the Anarcho-Capitalist way of life has to be normalized or desired, in the same way that people in the West would usually despise being under a monarchy, and if under one, would want to establish a Democracy.
The goal is to undermine the state, and for the time being, the best way to do that is to keep advancing crypto-currency technology. If people can protect their wealth from the state, even after being imprisoned/executed for tax evasion, then the state cannot profit from enforcing taxation threats. Fewer and fewer people work for the state as they realize it no longer has a source of income, and (those who sympathise with the Anarcho-Capitalists) instead work for Agorist institutions, most importantly protection agencies.
If that takes place, forming a new state would be impossible. You'd have to start with taxation or tariffs to fund your state, which is not possible when everyone's wealth is protected in such a way where only the true and rightful owner can access it.
What makes you think the Free Market won't just create a council for itself, and thus start a new government?