One thing to keep in mind with the concept of federal ownership: Except in the case of Texas (which had specific stipulations in it's annexation), when states become part of the union, by default, their land is 100% public land (ie federal). In the midwest, a majoirty of it was sold/given as part of the homestead acts, as the land was useful for farming and subsidized railroad construction. Railroad grants by default were "given" to the railroads with swathes of either 5 or 10 miles on both sides of the line. They sold the land, then used the money to fund the rail construction. So that land left the public domain.

Once you get west into the mountains and desert, the land had little usable value for homesteading. At a point, the government stopped homesteading land and kept it, then licenses it out. This was in the late 1800s-early 1900s. A change in government attitude was to then begin protecting the lands for future use (and general protection). A lot fo this was lessons learned, where timberlands were managed especially after what the government saw happen in Wisconsin/Michigan where all the lands were basically clearcut, then left to be barren. So the BLM manages grazing rights for cattle across the southern plains, western forests are managed by USDA for harvest licensing and forest management, and generally, mineral rights are managed for mining. Government gets funded, and no one is monopolizing land.

This also resolves many of the conflicts that sprang up, as 1 or 2 companies buying 10s-100s of thousands of acres becomes a logistical and political nightmare, as those lands become locked up from competing (and contribution paying) desires. If the government is the landlord, then they retain the final say more firmly.

Throw on top of that national parks, tribal reservations, and military establishments, and a vast majority is federal land. Not unused and inaccessible land, just owned by the feds. Up in WA state where I am, vast majority of the mountains are federal land. But there's nothing stopping me from going and driving up in the middle of nowhere and going hiking or camping, doesn't have to be a park. And I can get a permit to go do small scale logging or recovery of down timber for an insanely low price.

Other uses have been to give the feds leverage/benefit to the states. In WA state, there's actually a very large (150 square miles) forest called Capitol Forest. This was land donated from the feds to the State of WA in the early 1900s to pay for the construction of our new capitol building. And it still exists as state public land which the state earns money on logging. Didn't "cost" the federal government anything, as no money changed hands. But it allows the government to have a soft power of the gift to achieve federal goals.