Do these types of restaurants exist?

Host and guest, yes. But the waiter had no way to know whether the guy I was with was my date or not or which our financial arrangements were. He had no right to make my financial decisions.

I’ve got no problem with “don’t worry about the prices” (been both the person taking advantage of that and the person making the offer), but I do have a problem with the waiter being the one who makes that decision and I’ve got a problem with it being made on the basis of who happens to have tits.

ETA to the previous post: in that same restaurant, they did the same one time I was there as part of a group. The first menu (price-less) went to Sandy; the second one (priced) to her husbad Lew; by the time Anna opened her (price-less) menu and looked surprised, Sandy had opened her, looked surprised, looked at Lew’s, frowned, erased the frown and was requesting and requiring an “uncensored version, if you don’t mind” in the kind of voice which spells out “this is not a request”. So I know for sure that which menus to bring was completely a gender-based decision. Knowing what I do about the US service industry nowadays, now I’d speak with management - back then, it didn’t occur to us.

Yeah, I can understand being annoyed at the underlying sexist assumption to these priceless menus, because they do go to the women in the party, as far as I’ve ever seen… It’s not exclusively an American thing, though. I’ve also seen it in France, IIRC.

Actually, here’s a thread I found about them. Looks like France is a common place to see them, but they’re seen elsewhere on the Continent, too.