That actually seems useful. Not dividing by gender, but instead the idea of giving a different menu to the person who's paying and the one(s) who are being treated. It's tough placing an order when you're being taken out to dinner and can see the prices because you're going to avoid something you might really want if it's more expensive than the average of the menu.
I think that would be very hard in practice without prior arrangement. The restaurant has no way of knowing the circumstances of the dinner and the person doing the paying. Getting the most expensive thing on the menu may be a stretch for the host or it may of no consequence. (And the server won't even know if you're splitting the bill.)
If it's a place you're going to on a reservation you can work that out ahead of time. It wouldn't be something that would be the default at restaurants, but it's not impossible.
Yep, I did this for my mom one time. I was treating at a fancy restaurant, and I didn't want her picking based on price, so I had them removed.
I believe it's still common practice at private clubs, though i haven't been to one in a while. Menu with prices for the member, without prices for the guests.
That was another time/age, but it was certainly legal.