Well, in Western lands the land was owned by the federal government before they even were states. In other places the land was paid for - admittedly inadequately.
And for those concerned about the constitutionality of the government owning land, the government owned land before the constitution was even written.
Indeed Amendment 5, contemporaneous with the constitution, anticipates government ownership of land for public use. There is no more widely supported government use of land than the national parks.
Your third grader, who enjoys his playground, would understand the issue far better than your cramped soul.
I know a lot of conservatives and libertarians who are quite content to spend weekends enjoying recreation in our public parks.
I want to sell my share.
I thought you were wrong, but just to make sure I just re-read the 5th Amendment again from my pocket Constitution I keep right here on my desk. You are extrapolating. You are using the last phrase to attempt to justify Fedgov ownership of land, but that is not what that clause addresses. It is very clearly about "eminent domain" and the rights of owners to be "compensated". It is NOT about the right of the Fedgov to own land in perpetuity. See below:
"...nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use without just compensation."
That in NO way "anticipates" Fedgov ownership of open lands in that Amendment.
Then again, maybe I need to re-read the Body of the Constitution where it says that the Fedgov can own land. I may be remiss in my understanding. After all, the Colonists and newly formed Union did buy Manhattan, Louisiana Purchase, parts of Arizona and New Mexico from Mexico (Gadsen Purchase), amongst others.