And the reason they won’t do that is because because then everyone who didn’t win the lottery would decide not to go to Hollywood studios they day. They need more guests in the park than rise can accommodate.
You're discounting the cudgel of the reservation. People who have tickets paid for a day in a Disney park have to make a reservation days or weeks or months in advance. If they made the reservation for DHS for the following day, then, they can only go to DHS and no other park for the day... or, sit in their hotel room all day.
APers who have a reservation and don't show can lose their privilege of making reservations after a certain number of no-shows.
And how would not 'winning the RotR lottery' the night before be any different than being in DHS and not winning the RotR bang-on-the-server lottery?
Those with reservations are locked into the park. At least they know in advance that they do not have to show up an hour before the park opens for a chance to get onto RotR.