They are much more likely to enforce a protocol if a player bad or a good player on a bad team that isn't going anywhere. Then they'll make him sit. The more meaningful the game, the more likely they are to push you. In a playoff game for any player who matters it's a joke.
They want their good players to have long careers and not get concussions from waking up in the morning because they had too many already (like Austin Collie). It looks bad for the NFL, it opens them up to lawsuits, caring is a distant 3rd. Not that they don't care at all, the NFL isn't structure like a typical corporation (technically they are a non-profit I think lol). There isn't a bunch of red tape to make decisions or a structure that dictates they have an legal obligation to jealously side with what's best for the company. It's up to the 32 owners. And while some of them are uncaring scum, some do still have a bit of a heart and see their players as human. If enough of them see something as clearly wrong that will swing the opinion of the whole. But that is a very high bar. I imagine a lot of them see it as players making their own choices and trying to get their cash while they can. It's easy to justify things when you put it in that perspective to yourself.