The FS land was put into reservations to preserve watershed and to protect the timber for use. It belonged to the Federal government, in large part, being managed by what is now the BLM but was the GLO.
The BLM lands were basically, for the most part, lands that the GLO couldn't sell.
The recreational use and value of the FS lands came later, but are not a part of their originating act.
FYI, for the most part, all land beyond the original colonies was owned first by the US government and then sold; this is not a new thing.
Somehow, though, I have a feeling that there is going to be much bad feeling about this land sale (mostly because local people are going to be concerned that they will lose revenues, and potentially access, and that non-locals will be fighting because they don't want any of the public lands going private, where they have less sayso over how those lands get used. I wouldn't be surprised if they end up not doing it.
Tell that to another federal agency, the Tennessee Valley Authority, which is currently selling off land to developers, land it TOOK from families here decades ago.