I've stayed that late on a couple of occasions, most recently Spring Break this year (week before Easter).
DH had never been to WDW and HATES crowds. Staying in that late, the parks were all but deserted (after Spectro and Wishes) and we walked on to anything we wanted to! POTC, JC, HM - no wait! It was wonderful! (EP was open til 1a one night and there were still lines at TT, Soarin', and SE)
The first time I did it wasn't until 3 - it was when they had people pay for EMH. I think the park closed around 1a or so and again, it was wonderful! Little waits for all of the E-ticket rides. We rode Space Mtn 3 times in a row.
DH is bummed that the park won't be open that late for our next trip. He thought that was the way to go!