I think the assumption is that everyone should be given a chance. Specifically, everyone should be given an equitable chance. There are stories of female show runners being removed primarily because networks decided they were difficult or poor leaders; meanwhile, there are too many examples of abusive male show runners who full-on harassed very young actors with impunity. There are no examples of female show runners who have behaved that way because no woman would be socially permitted to do that.
Women would probably do better. Women would at least be far less likely to sexually exploit or scream or humiliate at their coworkers.
At the very least, women should get the chance to try.