In general you can do anything on the land that doesn't impede other people's ability to also do anything on general on the land. Permanent houses or crops would impede other members of the public who also own the land.
I'm curious why you exempted national parks and not national forest when the latter allows for even more use.
Personally, I use my public lands all the time, visiting several times a week and camping frequently. There's a 30K-acre chunk of national forest nearby we sold to a private corporation over a decade ago and now that's all cut off. They're just sitting on it. Used to be hunters and foragers and mountain bikers and motorcyclists and horses... Now all off limits. And what did we get in exchange?
I'm curious why you exempted national parks and not national forest when the latter allows for even more use.
Personally, I use my public lands all the time, visiting several times a week and camping frequently. There's a 30K-acre chunk of national forest nearby we sold to a private corporation over a decade ago and now that's all cut off. They're just sitting on it. Used to be hunters and foragers and mountain bikers and motorcyclists and horses... Now all off limits. And what did we get in exchange?