I think ideally they shouldn’t play because they will benefit from insider knowledge and bias, and will also form their own positive biases about characters their character becomes close to. But as multiple people have pointed out, that’s kind of an insane ask. Nobody wants to put in that kind of work for no reward.
In my opinion the next best thing is for staff characters to be totally anonymous. That way they can be just another guy in the background without getting mobbed by people looking to do a little bootlicking for brownie points. If their identity is known, they are constantly going to be thrust into the spotlight ahead of anyone else, and people will be afraid to oppose them.