It's been a while since I was on a dating site, but my experience was exactly that of a small amount of incoming attention, but almost all of it sincere. So yes, I think a lot of women would be happy to make that trade.

I just never saw a lot of the awful behavior that women get on the regular. E.g., the guys who will go from "u r hot" to "fuck you bitch" in a series of DMs over 12 hours with absolutely no response from women. It honestly amazes me that so many of them stay in the dating market at all.