If you think about it, there's something a little peculiar about a memorial to "Great Presidents." It's as valid a selection principle as any, but why not a memorial to "Great Americans?" In the end Rushmore almost comes off looking like as much a monument to the Presidency as to America or the four great Americans depicted.
But if you're thinking about great Presidents, you have Washington, and Lincoln, and it's hard to find others of that calibre. TR's being a very well known figure probably played a great role in putting him on Rushmore. If Polk or Jackson or Cleveland were up there, people would be forever wondering just who that guy next to Lincoln is.
And a collection of executive orders. It looks like the torrent of executive orders really started with TR. Earlier Presidents used executive orders for things we'd regard as trivial and procedural. Lincoln employed them for important questions of military governance, but sparingly. The quantity leaps up with TR, but they're still largely concerned with minor details. With Wilson and FDR executive orders increase and executive power penetrates far deeper into American life and society.