> In the United States, the government holds hundreds of millions of acres of land in trust...
True.
> ... and it needs to be relinquished in part to help grow the actual base of humanity they hold stewardship over
Almost entirely false. See, the land they hold, they hold because nobody ever claimed it under the Homestead Act. Nobody could figure out how to grow enough to feed a family, even with 168 acres of it. This mostly means that there's no water there.
I'm pretty sure that the solution to the housing crisis is not a few square miles of waterless sagebrush in private hands. If you build a city there, where are the people in it going to work? (If they're currently homeless, they're probably not going to get hired for the kinds of jobs where work from home is possible.) How is it going to integrate into the surrounding economy? Where is the food going to come from? Where are the roads for the food going to come from? Where are the power and the water going to come from?
And even if that is the answer... what private hands? Mine? I don't have the money to develop it. Blackrock's? The banks? I don't think you're going to think that approach is the answer, either.
(True, some of that land is forest rather than just sagebrush. But if the federal government sells it, it will be bought by someone wanting to log it flat for the timber. That won't leave it with cities on it, either.)