Teddy was put on Mt Rushmore to remind people of who was president when the statues were put there—Franklin Delano Roosevelt.
And Teddy was a Progressive, back before people realized that that pernicious doctrine used lies to justify theft, and then trends toward torture and murder.
Have you been to Mr. Rushmore. I’ve been there and if I recall correctly reading the background material from the architect, Gutzon Borglum, the real reason he chose Roosevelt was for the challenge of making his glasses. I kid you not. At least that is what the literature at Mt. Rushmore stated, again, if I remember correctly.
What he said the 4 presidents represent are:
Washington created the nation (the Father of our Country)
Jefferson expanded the nation (Louisiana Purchase & Lewis & Clark)
Lincoln preserved the nation
Teddy Roosevelt conserved the nation (established the National Park system)
But the reason I recall reading for putting Roosevelt on Mt. Rushmore was for the challenge of carving his glasses. Call this “urban legend” if nobody else confirms it.
That said, Madison should have been there instead of Roosevelt, the Father of our Constitution. But then, Teddy has a much more manly face, so there you have it.