I agree that the name has become problematic. I like the term "dominance-based culture" because it describes what the patriarchy essentially is without potentially making men feel defensive and/or confused. I just wouldn't want to lose sight of the gender imbalances that this culture promotes. While you're right that some women seek out "high status men," the question I would ask is, "Who has glamorized this type of man?" Men have run entertainment and media agencies for decades, so if there's a type of man that has been promoted as culturally desirable, I think we need to take a hard look at who is promoting this. Obviously, as women we have agency and can decide for ourselves who we're attracted to, but you can't deny the pervasiveness of the media when it comes to establishing what we consider attractive.