I usually don't need to stay in the room past checkout since we're 100% leisure travel so we're out sightseeing, but I'm usually not sure if we can leave our car without additional day charges....so I reached out to an upcoming stay and explained we were taking a morning walking tour and would not be back to the hotel until 1:00 or so - got a very nice reply that we are welcome to leave our car until 3 for no additional cost.
I've also often wondered for those of you who do need late checkouts....it would seem to me that "someone's" room has to be cleaned first, and "someone's" room has to be cleaned last - I would, when I got the dreaded knock on the door, would consider giving the housekeeper the tip I was going to leave anyway (or even a bit more) and ask if our room could be done last (having, of course, already officially checked out) - worth a try?