Except maybe some small land swaps or purchases, NONE OF THIS WAS EVER PRIVATE OWNERSHIP so your statement is factually wrong. Public ownership is good, just needs a bit better stewardship. And let's not get started about returning it to the aboriginal natives, American Indians, as they were never good stewards of the lands, not then, and definitely not now.
All of the ‘public’ groups (BLM, Forest Service, National Park Service, Tribal Lands, etc) are corrupted. Each has some lobby group that controls the whole game. Personally, I’d like to see a law where the feds have to hand over to each state with maybe some limit of 10-percent of a state’s property that could be controlled by the Feds and the rest controlled the state itself (I know it’ll never happen).
If you tried to cook up some land deal with the tribal units....it’d simply be turned into some resort hotel operation or gambling casino.