I've heard of this, but not for decades.
Back in the 1980s, a friend of mine was taken to such a restaurant by her boyfriend. That was the night he proposed, so he had planned a very special evening. He didn't choose the restaurant because they had the ladies' menu, but because it was one of the highest rated, most popular restaurants in the city at the time. And expensive.
My mother had been taken to a few such restaurants when she was dating. Her advice to me, for when I was similarly treated (never happened, though), was to choose a simple-sounding chicken dish, not the chef's specialty. That would most likely put my meal in the low-to-middle range of the menu. The goal was to enjoy your meal, but not put too great a burden on your date's wallet.