You can get the opposite extreme quite often as well, I'd think. How many really good lecturers have never proven a new important result?

I'm thinking of somebody like Grant Sanderson (3blue1brown), doing pure exposition extremely well. For that you at least need to be able to work through examples, or to present why an intuitive approach might fail, and these things can be little theorems themselves. It doesn't have to be publishable in the current culture of novel results, but you do need a lot of competence with the tools.