A fine idea.
You know, I am totally into this. And I live only a few miles from the edge of a National Park, where camping is forbidden (west section of Saguaro National Park). Unfortunately there is a dearth of suitable trees or other anchors. I leave to your imagination the concept of hanging a hammock from Saguaro Cactus. That idea could go in all directions, including the citation you would doubtlessly get if you got caught doing so. No, I don't think I will go there, but the potential photo op is tempting above all else ....
but as others have said, it is amazing how alone you can be just a short distance off of a well travelled trail. I have always made a point of "stealth camping" off to the sides of trails.
If you know how to read a topo map it is easy to plan ahead and predict camp areas where you will be totally isolated, often with a great view, even in heavily travelled areas.