So basically you're advocating for a more co-operative marriage where you both contribute in whatever way you can to each other, instead of the totally patriarchal one in the OP. You lead because you're a leader and your wife wants to be lead. What if the man isn't a leader and the wife is, why can't she make some of the big decisions if the man she's made a family with is just not that leader type of dude?
The wife pitches in her ideas and the man passes judgement on them regarding whether or not they should be applied to the household and whether or not they should follow them.
(simplistic example)
My wife tells me to take off my shoes when i come in the house. Like at the door. I used to not do this but its actually a good idea because over the years filth can generate on a carpet before you even Know it. I obey her in that regard.
I tell my wife do not Ever let my son sleep past 8pm. No naps after 6. She didnt understand at first but i had the insight to see that its keeping us up all night. So she obeyed and life is happier.
Im just speaking on my type of relationship. Im sure the relationship you're talking about exists but i have no experience with it because ive always been the leader in my relationship. I have some friends that came from a matriarch and none of them are married. They explicitly avoid women that want a leader and find women that come equipped with know it alll ness and so far, it hasnt worked out well for them. I literally dont know one thats married.
Its hard to be a strong man that believes hes intelligent and a leader and then have your woman tell you that you dont know what you're talking about and to fall back. It often leads to feelings of emasculation which cause the man to try to regain his masculinity through infidelity. On the other side the lack of good ideas and leadership from the man can cause the woman to be captivated by a man who exhibits more leadership qualities then her man.
Now if the man is just weak and his woman is not, then yea, i could see how that kind of relationship would work. Hes basically dating his mother, in a way.
I say all this to say that men should find women they can lead and women should find men that can lead them. A weak man, should start taking Brazilian Jiujitsu and reading proverbs every night.