The specialization of modern society would kill the idea. Everyone is a specialist in something, and there are a million different specialties. A hundred years ago, there were a lot fewer occupations. One able-bodied man could do most jobs.
On the flip side of the original question, I would actually prefer that men not be allowed to work certain jobs, which have been traditionally female, like nurse, receptionist, flight attendant, secretary, day care, or elementary school teacher. I think women are naturally better at those jobs, just like men are better at a job like fire fighter, carrying unconscious people out of burning buildings.
That's the joke of Feminism in demanding that everyone is equal at everything - it robs women of recognition for being better at some things than men.