Legality of living in the wilderness?

Stop thinking parks. Think BLM. For example most of the state of Nevada is federal land. You are free to camp there. You are not free to build a structure. A park is also federal land but it is regulated and maintained. Other federal land, owned by the Bureau of Land Management, is considered wilderness and is available for general use. You cannot mine, or build a home, or make improvement, or engage in logging, but you can certainly camp. There also may be restrictions on fires at least some of the time.