Hard to manage a double header when there's a 4:00 game already scheduled,
Typically, if there is a 4pm game, and they really want a doubleheader, it's a traditional doubleheader with the 4pm ticket holders getting both games. Second game might start a bit late but they don't complain because they are getting a free game. Depends on how much management wants to get the game in, because they lose a gate, but on the other hand it's good for fan morale. I've twice been the recipient of a free game in this manner.
Of course then the complication becomes what happens to the tickets for the rained out game, since there is no makeup. In the past, they have offered to simply refund in full. I don't know .if they would still do that