I was in Anchorage the other day with checkout looming at noon and my flight out not till 10 pm. I asked for a late checkout and was offered 2 pm. When I asked if later would be possible, I was offered a half-day rate. This seemed like a very good compromise to me and I kept the room till 9 pm. Had a nap, took a shower....
Seems this is quite common in Anchorage where flights often leave late in the evening. I was happy to have the option. But I guess no half-day credit!