Well what'll end up happening is you will use the army to control territory and extort regular tribute from farmers in exchange for you protecting them from other raiders + you not taking their stuff. You can also provide your army with stolen farms, and call them up to service when needed. Congrats, you are now a feudal lord.

This is what the current government does but in the post-apocalyptic world it'll be less fair and more expensive.

The reason why government exists is because it solves very real problems. If there is state failure, we're not going to devolve into a libertarian utopia. What is more likely to happen is what has already happened in countries such as Somalia or the Democratic Republic of the Congo or Western Europe after the fall of the Roman Empire.