I guess it gives it similar gameplay to an infinite runner game on a mobile phone, which could be interesting in the context of a NES game. Have you thought about maybe making the character unable to move left? Maybe have the d-pad do nothing at all, and he just runs right on his own -- so it becomes a one button game?
EDIT: I say that, and then I remembered there's exactly one screen where you HAVE to to turn left to jump up onto a platform behind you.