I'm hardly stuck on payriarchal ideals. If the woman asks the man out first and he accepts then she plans, makes arrangements and pays. She's the bost and he's the guest. After that first date, or first few, then you can alternate, split the bill as agreed upon by both parties, or whatever.
Most people when the start dating these days atenmeetinf odf of apps or what have you. They don't really know each other like they used you. That's the reason for the formality. Not patriarchy. It's almost taboo to talk about money with strangers, yet we date strangers. So there's got to be some give there.
Further, you keep blaming women for being stuck on patriarchal ideals while absolving the men they're dating of the same. Not many people are into kink. You've for different rules. That's fine for you but your rules won't apply to the rest of us. You're forgetting that many if not most men feel emasculsted when a woman asks them out and how they have a tendency to act up in various ways to reassert themselves.