Once a state was admitted to the union, the Feds were to sell, offer as homesteads, and otherwise privatize the land, so that the people benefited. Any revenue raised could thus be used to pay Federal debts/contracts.
The current Federal “ownership” is unconstitutional. The Feds tried this with Missouri and several other states, but the states banded together and were successful in forcing the Feds to divest.
“The land rightfully belongs to the people”
By what right? Did the people buy it or inherit it? Did they conquer it? Of course if by “the people” you mean the people of the United States, not the people of an individual state, the answer to my last two questions is “yes”.
“not to the government (state or federal).”
We agree there.