> Out of curiosity, what can go badly? They offer a counter and then fire you a couple months later, after they've found a more "loyal" (or just cheaper) replacement?

Definitely they question loyalty. In general all companies have an expectation of loyalty from employees they will throw away at a moment’s notice without any remorse

I leave jobs for two reasons: abusive employers/coworkers ot money. Because of this I would never accept a counter-offer, obviously I wouldnt stay in an abusive alsituation, and if another company sees me as more valuable than my current employer then the fear of losing me won’t change my soon to be former employer’s view.