How much influence do deans have at Stanford? I think she's a great teacher, but from my experience, your teaching ability is irrelevant when it comes to your responsibilities as Dean.
I have no experience being a dean. I do have experience being managed by one. I personally didn't see any correlation in their effectiveness and their popularity as a teacher. If you have any evidence stating there's a correlation I'd love to read it.
I'm sure there's some correlation between teaching ability and money raising, one of the more important aspects of being dean. They both stem from being a good people person.
Maybe she was promoted to Dean because she's incredibly well-rounded, has a solid vision, is of great character, has cultivated numerous productive working relationships and can fund raise like no other. She can be all that and a great teacher.
She was the chair of the cs department for two terms and did a fantastic job by all measures. Teaching skills aren't why she is qualified. Past administrative experience and success are why she is qualified.