"Imagine if there were no governments" is a category error. There are always governments, not all of them are formal. Whoever has the most mercenaries can make rules.

The thing that works is to have a coercive force which is primarily used to quell other large coercive forces. So you have a police force that prevents violence etc.

But it needs to be limited in scope, because it has no natural predators. It's always tempting to use the coercive force for <thing> where <thing> is literally anything. Laws are molasses. They have benefits, but they also have costs, and the fact that the costs and benefits apply to separate people makes it much too easy to do net-negative things.

> Imagine if there were no governments.

Then someone would assume that power. Anarchy is not stable.

> Big companies could hire mercenaries to enforce their contracts

In the absence of any other government, any “company” is a government unto itself. And any that raises an army, by whatever means, pretty quickly makes that even more clear.

You dont have to imagine, just see what happen in relatively weak governments: Drug cartels, war lords, mafia syndicates, union busting, etc, etc. This is just a hunch but I wouldn't be surprised if the biggest part of actual monopolies is enforced by illegal means.

That's the exact scenario that I would love to ask an ancap about, tho unfortunately I don't know any to ask.