One thing I've always wondered about is the possibility of a Texas-Czech fast food place based on kolaches (really klobásník, but who's counting?), which is basically a doughy wrapping around a filling (greatly varying, from something sweet like Czech kolaches to something savory like sausage or eggs, similar to a sausage roll or corn dog). Very very adaptable to drive-through use, easy to eat with one hand and not too messy either. Seems like the perfect fast food to me, but they're a very regionally Texas thing, or have been until recently.
Incidentally, this is a big reason that fast food places would never serve beer...they are, at their core, built around the drive-through, and even in the 1930s selling alcohol to someone in a drive-through sounded like a pretty bad idea. Plus, the patchwork of liquor laws in the United States would make it extremely inconvenient and require getting liquor licenses, which would greatly complicate franchising. Best to avoid. Generally speaking, a lot of the discussion here seems to be ignoring the importance of the drive-through and in-car eating to the rise of fast food (but I suppose KFC doesn't quite match this either).