Yes, some women hit on men but the frequency is a lot higher in the other direction.
Quote from “Can I Buy You a Cup of Coffee?” may help put it in perspective:
“Thing is, when it’s not scarce, then even the nicest act starts to get annoying. Because you don’t get to control when people are quote-unquote “nice” to you, and it happens all the time, and you know there’s always a hidden cost behind it. You start to question people’s niceness, because they’re not doing it to be kind, they’re doing it because they want something from you.”
His follow-on story, “But if I Can’t Buy You A Cup of Coffee, How Will Our Species Reproduce?” is entertaining enough just in the title.