I was just thinking of this the other day, so thanks for being of like minds!
I was thinking it could work if the format was similar to Friday the 13th The Game, but with some twists. One of the twists would be that if you fall asleep you end up in Freddy's Nightmare world where everything is out to kill you to a point, obviously this would play like a good Jason chasing a counselor scene but with crazier stuff happening all around and behind your character "RUN, Nancy, RUN!"
I think there would definitely have to be two modes for a Nightmare on Elm street game to be true to the franchise, Asleep and Awake. If you all remember in the movies, not all delusions killed the kids who fell asleep and there was an element of Freddy screwing with them before going for the big finish kill. I think that could work to a game's advantage perfectly with the right timing and balance.
As far as gameplay goes, I'd love to see a scavenger hunt style gameplay, again similar to F13 where you search for items to help you stay awake and ultimately defeat Freddy. Items the kids of Elm street could look for would vary but would include caffeine pills, coffee, drugs in general to stay awake and Freddy's bones wherein you need to collect so many of them and put them in the furnace to kill him for the match. On the flip side, I would imagine that here and there a caffeine pill might be confused for a sleeping pill and could be a pitfall of being tired and awake for so long.
Maps could be similar to F13 and include Nancy's house, the high school, the psyche ward, and the seminary, with maybe a Camp Crystal Lake map for good measure! I think the folks at Gun Media could totally pull this off and I would not be surprised if they haven't done a mock up for a Nightmare on Elm Street game already. If anyone has seen it or can link it in reply that would be incredible!
Each character would play the map like F13, but instead of finding dead bodies they could find dead or sleeping bodies and try to wake them up if they have the right items. A minigame perhaps where they have so much time to wake them before they are killed even might be cool. I think it would be mindbending to be playing and not realize you or someone is actually asleep in the game.