Tony shows him the letter that Steve sent him, wherein Steve requested that Tony A) help Bucky B) have the Captain America legacy continue (from an in-universe perspective, as an aside, while Steve is most certainly the best at the job, there's an idea with some currency among fans and writers that being Captain America is something only Steve can do, which to me seems wholly at odds with the idea of American values). Tony, always looking to cut corners, wants to kill two birds with one stone
Not at all in my opinion. In America according to our values anyone can become great. That does not mean that those greats can just be replaced. There was only one Washington, one Lincoln, one TR, only one FDR, only one Grant, one Eisenhower, only one MacArthur. And so on.
And that kind of adds to a feeling of irreplacablity. You may add your name to the list, but since you don't knock the other guys off comparisons remain.