What is the problem we're trying to solve with this?

Anything short of enforcing some sort of anti-shitposting policy on signature campaigns is probably not worth the effort. Bad managers will be bad even if you give them good tools.

For example the forum could track how many users in each campaign got banned or had their posts deleted by mods and adjust certain privileges based on that, e.g. limit the number of users they can hire. But that would basically require EVERY signature to be approved by the forum, which I guess goes against the "no screening" stance.