I'm not sure where you are but I don't see the power shifting in favour of men at all. All I keep hearing is a bunch of men complaining about not being able to get a date, all while investing very little effort into it or into their personalities. By the end of the day, most women I know are interested in a good partner, which is rare to find.
I'm going to tell you a secret. Are you ready? If a girl has sex with a man, it doesn't always mean she even wants to see him again. If the sex was semi-okay, then maybe. But most of the time, at least according to my female friends who go for casual sex, men underperform, and they don't want to see them again. Only naive and delusional people believe that sleeping with someone will get them a relationship with that person, regardless of gender. Also, only the most attractive men, as in maybe top 10% of the dating pool, have a chance at sleeping with a bunch of women; most don't unless they get lucky. But if a woman is looking to casually sleep with someone, it's not because she wants to date him, lol.
I don't do hook-ups, but if I did, I surely would go for men whom I would never even consider dating. Because it doesn't even matter much if I'm seeing them for 2 hours and not gonna text them again. But according to the said casual-dating-female friends, most men fail to get casual sex even when it falls in their lap, or end up screwing it up. When I hear the stories of how little social skills those guys have, it's hilarious and sad at the same time.
The difference is that I, a pretty average looking woman, can get sex if I go to the nearest bar, in an hour. Most men don't get that luxury - or more like sadness, because banging a stranger won't get someone to love you or care about you. So, even if we're talking about seeking casual sex, the women still have the power you're talking about. Also, calling it "power" feels odd, this is a very specific red pill lingo here, lmao.