Fortunately, the terrain is the limiting factor. There just aren't that many places where it's practical to set up a tent. They went to a lot of trouble to build tent platforms for a reason. The choices are extremely limited on the Franconia to Madison section, as most of it is above tree line or damn near it. Sure, there are a hand full of places where people have obviously camped, but these places aren't something you can plan on using.
The other thing to consider is this is a very active trail and these few sites are directly along the side of the trail. Otherwise, you'd never see them.