I understand your points, but in my opinion, the vast swaths of public land that are available to EVERYONE to recreate on however they want, within boundaries, is one of our countries greatest assets.
Let the states own it, and I'd be willing to bet my life that all the above would change drastically for the worse.
Humans, especially Americans, have historically been fantastic at destroying wilderness through extraction or consumptive resource use, without anyone holding those parties' feet to the fire in restoration and damage mitigation. I believe that would be even worse under state and private ownership.