Surely 'the power that men have over women' is dependent on both the men and women in question and where they are.
Privilege is not complicated. Society is.
Let us take the middle aged wealthy white women and the beautiful but young Mediterranean lover she has taken. Who wins? Who has the privilege? The white woman with the wealth? Or the young man? Doesn't it depend on the wider context? Doesn't it depend on knowing a little bit more than just 'men have all the power'? Who has the privilege in the soup kitchen I cook at? The white and asian women who make up most of the work-force, or the homeless folk who come for a hot meal. Many (but not all) of them men? Are you prepared to argue the wife of a local millionaire has less privilege than the homeless guy she's serving? I suspect you are.
For what it matters, I don't mind a bit of reductio ad absurdum in my arguments - it makes them fun to read.... but as you've quite openly stated you believe that men are always the problem and that you'd make them give up their power (without any underlying thoughts about the complexity of interplay between individuals) I think we can safely just put you in the tub thumping misandry camp.
And that's fine. Misandry is absolutely fine as a world view. It just isn't feminism.