This seems only marginally better than buying a vacation time share. If you "own" one of those, you are supposed to be able to swap for another (either location or time slot). This only works if someone wants your slot (not necessarily the person who owns the slot you want, but still, if you have a slot/location nobody wants, you are stuck).

On top of that, you are proposing some kind of federal ownership. To the extent fed properties are immune to local taxes, you are asking other property owners to subsidize this (localities typically have to pay for schools, police, fire/emergency, libraries).

To be fair, if you buy a time share, you still have to pay "maintenance" (often about what you'd pay to stay in a hotel for the same time) and at the end of the "term" (10 to 20 years) you own... nothing - so it's a spectacularly bad deal. The author's proposal leaves the owner with a bit more than that, but only theoretically.