This is all such easily accessed information direct from NFS, NPS, and BLM government websites, it's impossible to not view your comment as written in bad faith. Public lands are broadly your lands to enjoy and use as they exist in their natural state, so long as you're not depriving others of the same access.
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?
If you are not constrained by a vault toilet and pack your own water, it is a playground.
It is shared ownership. You want to build private property on land that everybody owns?
So if it belongs to me, can I build a house there? Plant crops? Go hiking or camping? Can I do these things whenever I please without asking anyone? Because I wouldn't say "that land belongs to me" in any meaningful sense. National parks aside, I don't see how citizens benefit from the government owning large tracts of land.