I would take your idea a step further. I believe that even the states should forego land ownership. Private property ownership is what distinguishes a free republic from all other forms of tyranny. The feds, the states, the counties and the townships/cities/etc. should not be in the business of competing with citizens for ownership of these assets. Period. End of story.
There's a big difference between States ownership and what/and how the Feds own and regulate property.