I mean, Washington is pretty much automatic due to his being the first among the founders, as is Jefferson for the fact that he basically built the entire idea of the United States of America in his head before putting pen to paper so others could realize his dream. Lincoln's presence is fine as a cautionary example regarding the abuse of power, so I don't think we need Obama or GW Bush on there since they'd be redundant (Obama for his hostile takeover of the healthcare industry and 10-20% of the GDP, and Bush Jr. for his ridiculous invasions into the last vestiges of privacy we once enjoyed).
But how in the name of the 1976 Seattle Mariners did Theodore Roosevelt get on the thing? Having read his Wiki page and remembering what little I learned of him in scholastic studies, he strikes me as a guy with 10/10 in PR skills and not a ton more. The Panama Canal was cool, but I dunno...my immediate reaction whenever I see Mt. Rushmore is: "One of these things is not like the others."
And just to be clear: I hate, hate, HATE Lincoln with the fury of a type II supernova headed for a black hole, but he at least was unthinkably impactful on the history of the USA (or its death, depending on your perspective; the USA post-Lincoln is nothing like Jefferson's beautiful dream). Even as a little kid it was hard for me to declare Lincoln to be the greatest president (though I'm sure I did so at a teacher's insistence on more than one occasion as a 6-7-8 year old) simply because it seemed to me, at that age, that if he was such a great leader he should have been able to navigate the situation without declaring war on his own country. Even as a child that struck me as incredibly tyrannical, though I wouldn't have used that word then (I probably would have used some form of the word 'bully').
MLK, if he'd been president, would be a fine choice - superb even - but I think Rushmore should be reserved for presidents so I wouldn't put him up there. Wanna set up a new monument like Rushmore? Be my guest! Put Pocahontas or Sakajuwea on there if it floats your boat; either one deserves entry into the conversation of impactful natives (though I realize Pocahontas was prior to the USA's existence). MLK would be a fine entry for there as well, as I think would John D. Rockefeller, Andrew Carnegie, or Ben Franklin.
And as for the M's Mt. Rushmore? Edgar for sure, Griffey almost for sure, Felix for sure and Ichiro for sure. RJ's got a great case, but it's true that he went from the Big Unit to the BIG UNIT!!!!!! only after he left here. Still, for me it's a toss-up between him and Griffey; RJ was the better overall player and enjoyed his greatest success after leaving, while Griffey was (in my mind) a tick lesser overall but did almost all of his good work here before leaving. So I guess it'd be:
Edgar
Ichiro
Felix
RJ/Griffey (I could probably be blown one way or the other by a three year old's sneeze)
And, now that I'm thinking about it, Pat Gillick and Lou Pinella might deserve placement...but that's muddying the waters. Still, they were the only ones who would speak truth to power and actually tried to win here by any means necessary (I don't include the players in that blanket statement; I think they try to win every single pitch).