In regards to the question of whether professors should be managers or monastics: professors are essentially managers. Supervising a research group is engineer

In regards to the question of whether professors should be managers or monastics: professors are essentially managers. Supervising a research group is engineering manager, product manager, project manager, marketing manager, career coach, and fundraiser all in one. Most professors aren't trained in management unfortunately, because one doesn't (usually) learn those skills during a PhD. Most generally accepted management techniques would make any professor more effective. (source: I have a PhD, worked in research including briefly as a professor, and am now in a startup)