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.
But that exactly anticipates public ownership of land.
In the second point, remember that our constitution is built on the common law of Britain, which was our legal system at the time of founding the country. "real estate" means, literally, land owned by the crown, and granted as an estate to an individual in fief to the crwon. The notion of crown lands or government land is so pervasive in law that it was not considered worthy of separate mention. Some things are so fundamental they do not merit mention in the constitution - your right to breath the state's air for one.