Given that these lands being public dates back to the earliest days of our nation, this is pure nonsense.
It's funny how you can't read your own definition: "a political and economic theory of social organization that advocates that the means of production, distribution, and exchange should be owned or regulated by the community as a whole." Socialism is a system where the government owns the means of production, like factories, farms, etc. It has absolutely zero to do with the government owning land. You are simply wrong.
Let's also note that you completely ignored my key point: nothing government does benefits everyone. That's because you don't have the foggiest clue what you're talking about, and are just parroting random wing-nut talking points.