I know many more women would mind. Many more women would mind dating a guy who is less successful than she is.
There is also the problem when couples get married. They both start off roughly at the same level, but when the wives outshine their husbands years later, they often make it clear that they think their husbands are losers and should shape up or risk getting a divorce. Then when the divorce happens, they blame the husbands for being male chauvinists for not being able to accept their success.
I am glad I manage to take the easy road. I did better in my career than my wife and so do not have to worry about this issue. Now, we are pondering about my wife quitting her work and working flexi so that she can spend more time with the family. Money is no longer an issue for my family since we have enough of it.