“Should they split the cost of each date or should they switch who pays from one date to the next?”
That’s one possibility but does present other problems. Less problematic possibilities include the women thinking of a place to go (cheap one), meeting the men half way, making a picnic. The point is, if one is only giving, and the other only taking, you are not going to have a healthy situation. Also, she can make sure she eats before the date and they can just go out for a piece of cake.