An interesting thought experiment. I wonder if you think that this hypothetical mint would be treated any differently than West Point? I believe that there are a seven or so modern day commemoratives that have been minted at this facility. The West Point Academy Bicentennial was an obvious choice to be minted there, and the Statue of Liberty commemorative kinda makes sense, but I'm not sure that I see as much of a connection with the Mt. Rushmore commemorative.
"If you climb a good tree, you get a push."
-----Ghanaian proverb
"The danger we all now face is distinguishing between what is authentic and what is performed."
-----King Adz