being a better teacher, makes me a better researcher and vice versa.

I think this is an underappreciated/underrecognized truth. A lot of awesome researchers (professors) at a place like this aren't nearly as invested in teaching as they are in research, and so even though they COULD be great teachers, and that potential is partially related to their rock-star researcher abilities, they are often NOT great teachers.

The connection between good researching and good teaching should be stressed more in grad school. The attitude adjustment would eventually work its way up through the pipeline, and I think that's the most efficient way to do it.