The entire country is for “First Amendment activity”!
Such stupidity.
I don't disagree with your point. In principle you are right.
However, the courts for many years have determined that when government agencies do certain things, they create “free speech zones” in which the government cannot create regulations which have the effect of restricting politically unpopular expressions of views once they have allowed politically popular views to be expressed.
In other words, a regulation which might be acceptable in most places becomes unacceptable if it has the effect of restricting free speech in a location where free speech has traditionally been allowed.
In this case it looks like the creation of a “free speech zone” gave the National Park Service the legal “fig leaf” needed to justify opening the World War II memorial as an exception.