You are absolutely right. Making more doesn't mean you save more. And to be honest, I have ended some first dates because the guy allowed me pay my bill when I offered. But it's always because I didn't like the men. If I like the man, I will be blunt that I don't fancy paying my bill when you ask me out.
If I ask you out, I pay and if he insist, I let him. Then buy him a gift instead. I do this because I don't like people getting entitled to my time or anything .
But not all women are like me so I get where you are coming from. And like you pointed out, gender roles can be conflicting. However, more men are beginning to give women their due respect and that is what’s important. We’re moving away from toxic one sided partnership to equal partnership.