[BroJoeK]

tacticalogic: "If the federal government has to pay property taxes on the property it owns in a State..."

Good point!
I agree that would be better.
But my guess is that Eastern states which have very little Federal land, probably wouldn't like Federal taxes being paid disporportionately to Western states and Alaska.
So it's all politics, with the usual result that nobody is entirely happy with the solutions.

[tacticalogic]

But my guess is that Eastern states which have very little Federal land, probably wouldn't like Federal taxes being paid disporportionately to Western states and Alaska.

The Western states and Alaska probably don't like the Eastern states having more say over what happens to large parts of their territory then they do. If the Eastern states don't like the idea of paying the property taxes maybe they'll think twice about voting to have more of it taken over, or getting some of it back in to private ownership.

As I said earlier, you can't have a working republic if the national government can arbitrarily take resources of the member states. We're guaranteed a republican form of government in the Constitution. You can't very well claim to have that without a republic.