The US government, especially the forest service, is the most environmentally-degrading land-owning body I can think of. Do you think environmental quality in the US would improve if all public lands were auctioned off?
Of all the national forest lands in the US, only 3 are profitable.The rest of the cost is paid for by US taxpayers, the only profitable lands are those which have extensive drilling rights sold. While you can say that the government fines those that violate it’s policy’s, in reality it does not. Look at the stats of polluted streams from drainage. State forests are better preserved than fed forests. If you look at privately-owned forests and timber lands, they do not clear cut to nearly the extent which the forest service allows. Any entrepeneur could tell you that this is a waste of money and of the long term viability of the land.

Groups such as the Nature Conservancy would buy the most aesthetic of lands I would imagine. When the NC leased drilling rights, it was far less environmentally destructive than the pumps in forests such as Allegheny, and they used proceeds to buy more land. Look at what International Paper Co. has done with it’s lands, I am out of room to type.