Because as we've seen the 'public' land is actually materially controlled by a tiny minority, many of whom are in cahoots with corporate interests, which is now coming to a head.
Since it generates next to no revenue as a public park it doesn't take much cash by exploiters to curry interest. If it isn't doing anything profitable nor in the private hands of say some rancher that will chase off ne'er do wells it is in jeopardy to whoever has greatest access to corruption.
This is such a weird objection. I'm sure national forests and BLM lands could be better managed, sure. But I can still camp, bike, motorcycle, raft, canoe, swim, hike, climb, ski, etc etc etc. I'd rather have poorly managed land I can use than a bunch of no trespassing signs.