This post was also discussing lunch where, presumably, eating while driving is less of a big deal. (Though, yes, some Americans eat in the car a fair bit which makes sandwiches and the like more suitable.)
It's not as ubiquitous as McDs, BK, etc., but pizza and Chinese are among the most common fast food alternatives to the primarily sandwich chains. (Fried chicken is the other.) And neither Chinese nor pizzas are very amenable to eating while driving.
I guess I'm conditioned to think of fast food in terms of drive-through. Even KFC has a lot of stuff on the menu that can be easily eaten in a car. Taco joints are the same way. Heck, the Greek place I mentioned was a drive-through.
When I think pizza, I tend to think of it as its own thing given the whole delivery culture.