Does Society Use The Mt Rushmore Exercise Incorrectly?

Typically when someone is asked to name their Mt Rushmore for a given topic the results are the four best or four standout examples. However, the four presidents depicted on Mt Rushmore were picked because of their role in preserving the Republic and expanding the territory of the United States. They were not picked because they were the four best presidents up until that time or representations of four unique areas of development for the country. Maybe Washington, Jefferson, Lincoln, and Teddy R are the four best examples to represent four distinct periods of growth in the country but the justification seems a bit flat. Hell, Teddy's up there at the request of Calvin Coolidge.

I don't know what the structure should be in the Mt. Rushmore Exercise but the way it is used now seems counter to the origin.