The only thing an authority figure, face and heel, really needs, is an actual motivation that's consistent.
William Regal has the motivation of wanting a clean wrestling show that runs smoothly and fairly. Thus he gives fair opportunities to faces and heels both, if they've earned them, and people who haven't earned anything get the chance to do so. So he's a face because he's upstanding and honest.
Dario Cueto wants to make money, and he does this by promoting matches and shows that fans will pay for. So he gives faces and heels alike the opportunities in order to make big matchups to make him more money, and gives no shits about the welfare of his wrestlers in the process. So he's a heel because he only cares about his greed and has no morals.
Stephanie and HHH want...something. What is it has never been defined, now is how they plan to achieve this undefined thing even more so. They are just there, making random matches and never having any consistent motivation or logic behind them. They shit on faces then give the faces free opportunities. They support heels then shit on said heels in the next segment. They constantly talk about being best for business but never actually talk about making money and constantly do things that accomplish the opposite.
Vince used to have this, it's what made Vince vs Stone Cold so great, but eventually he just devolved into a cartoon villain who does shit because they need shit to happen.