Wikipedia has a map of the ownership of federal lands here: https://commons.wikimedia.org/wiki/File:US_federal_land.agencies.svg--basically https://commons.wiki

Wikipedia has a map of the ownership of federal lands here: https://commons.wikimedia.org/wiki/File:US_federal_land.agencies.svg--basically https://commons.wikimedia.org/wiki/File:US_federal_land.agen..., the yellow lands are the lands never sold and largely represent the stock of available federal land. The green lands are parks and US forest (which is often, but not always, parkland as well in some sense); the red isn't the federal government's, it's Indian; and the other land is owned by agencies for their own purposes (most notably the military, and the resale value of former weapons testing ranges isn't great). As you say, a lot of that yellow land is basically desert or semidesert and uninhabitable. Although that understands the nature of the problem, since the US did manage to sell off a large swathe of uninhabitable land--the High Plains was sold off in the late 19th century, only for the Dust Bowl to happen and people to realize that in fact, no, this wasn't good farmland.