Granted, most campgrounds are full on weekends between Memorial Day and Labor Day, especially the popular ones. By the same token, they are pretty much ghost towns during the week. The trick, at least around here on the right coast, is to pick a campground that still has first-come-first-served, ie, unreservable sites. Then do your traveling on Tuesday-Thursday and stay put over the weekend.
For the last 5 years, I've hosted at an NFS campground that has been wildly popular for decades. About half our sites are non-reservable. Even as popular as it is, it is never full mid-week.
As for the paucity of boon docking opportunities here in the east, 'tis true they are hard to find, but they do exist, just perhaps not where you might want them to be. The Washington-Jefferson National forest not far from where we live has lots of them, some in designated campgrounds, some in "dispersed camping" some free, some charge a nominal fee. Few are easily found via the internet, however.