They definitely can add anticheat to cooperative games, though again it feels a bit much.

I would say not to worry too much? The potential for abuse exists, but is not actually used. The companies that make the anti cheat software these days have way too much on the line to risk that kind of behaviour. It's one of those things that it's in a bit of a weird state, and some people like to keep an eye on it, but for the vast majority of cases is a minor inconvenience.