I think to some extent the OP's problem is that the difficulty of having a colleague get promoted to being your boss, which isn't really a problem unique to medicine, but is worse than usual in medicine because residents tend to share more with each other than normal coworkers.
Chief is a weird position. Residents don't have as much solidarity as you might think they would, but in my experience they do at least share a very vocal distain for all things in residency. The endless documentation. The pointlessly long abusive hours. The attendings. You also learn more than a little bit about how different residents actively shirk the system, and the problems in their lives that are keeping them from caring about doing better.
Then you're chief, and you know all of this these things told to you in confidence by other residents as a co-resident, and you're still getting told more stuff in confidence because they still think of you as resident, and what do you do with it? After all you're supposed to be the boss now, the system's designated cheerleader/organizer. You're now held responsible for not just yourself but also everyone else's behavior. Say for example that you know PGY-2 Schmuckatelli is having other people sign in to morning report for him because he told you when you were a PGY-3. Do you bust him, or ignore it because you learned it as a resident? Do you ignore it indefinitely, even though you're seeing it every day, because it was a preexisting confidence? What do you do when other people stop showing up because they see Schmuckatelli getting away with it?
What about personal problems? You have a friend who comes to you and tells you he's been late all the time because he's about to get divorced and is getting depressed, but he doesn't want to see anyone or change anything. Do you keep that a secret? If it is a secret, do you bust him for being late and ignore what you know he's going through? If not how do you look like you're not playing favorites? Do you make excuses for him? Do you try to reschedule them for lighter rotations so they can deal with things? What about when people ask why you're doing what you're doing? Its hard to think of a way you could handle this where someone wouldn't think you handled it wrong.
Then there's just the question of attitude. What about when people just come to you to complain to you about the same crap they've been complaining about for the last 2-5 years? Do you take the party line ("well I hear your frustrations but actually those forms are really useful tools to improve our model of education") and risk sounding like a dingus? Do you continue talking badly about the system, like you were a resident, and risk that they might take it as tacit approval for bad behavior?
Again, its not a problem unique to medicine.
Every 19 year old lance corporal has to deal with the magical moment when one of his buddies suddenly becomes his boss. I'm not sure there's a good solution for how you want that person to act. Honestly all you can hope for is someone who is consistent, who lets you know exactly how they're going to act early and then sticks to that. The only objectively bad way to be chief is to be a different kind of chief on different days. Or worse, with different people.