The rule could be anything, as funny or as serious as you want. The universe will progress in a similar way that it has up until this point, unless your changed rule prevented it from doing so.
Some examples might be:
- The invention of currency is not allowed.
- Iron is slightly less stable.
- The Ancient Greeks are able to cultivate Silphium, which does not go extinct now.
I wouldn’t classify “teacher” as a “position of power” in the sense that people who are mostly interested in holding power over others want the position for that reason.
There’s a huge difference between “being interested in power” and “being interested in improving things for yourself and other people”. The one is selfish in nature, the other isn’t.
There is also a huge difference between wanting a position and being good at it.
And yet, instructors and teachers are in a position of power over there students. A bad teacher can ruin a subject for you, destroy your grades, and get you in trouble. I believe it fits within the definition.
That is the exception and not the norm