Folks who have never been to the White Mountains or north of there may have a hard time understanding the terrain.
The upper third or half of the mountains are either bare and flat (rocky ridges) or bare and steep, or steep and impossibly uneven and covered with insanely dense, stunted growth (krumholz.) On the steeps you will be severely challenged to find enough even ground for a tent, and the growth will give you no cover whatsoever (nor place to hang a hammock.)
Yes, you can find safe and legal camping in the hardwoods, but the hardwoods end a couple thousand feet below the summits.
There are several non-hut options, eg. Liberty Springs Campsite, Garfield Ridge, Ethan Pond Shelter, Guyot, The Perch, Imp, etc. These provide (safe, legal) refuge without requiring quite as much descent.