My theory is when women and lower class men started working as bookkeepers and accountants in post war America a way was need to keep the plumb jobs reserved for the fail sons of the privilege classes.
I could be wrong but while 'business schools' existed before then the MBA as a upper class ivy league thing exactly dates to that time.
Wasn't it also a time of larger projects being started, which required more coordination? Not that your theory needs to be wrong, it could be amplified.
Whatever the reason it is definitely not because they are effective managers.
I suspect it's more of a social class phenomenon - they speak the language of the ownership class and that engenders trust.