First of all, I'm not a natural science manager, so I'm not answering this question with direct experience in that vocation. But, I have been involved in scientific research for several years. It is not uncommon for people to take unconventional paths to their current position, so I wouldn't rule out a pure mathematician becoming a natural science manager, if that person has the right experience. As far as working less and being overpaid goes, people say similar things about a variety of professions. I think it is not so much professions, but individuals, that matter. Some will be hardworking no matter what their vocation is. Similarly, some people may not be as hardworking, regardless of their profession. I suspect you will find a range of opinions that depend on who you talk to, all of which are colored by their own, personal experiences.
All the best,