RDJ's a good actor, he delivered a good enough performance, but he was essentially playing himself. 616 Stark is a moderately "tall" (6'1"), built guy with steely eyes who is more often than not aloof, cold, manipulative and has bouts of depression and anger fits. He's no Kylo Ren or Doom, but he's not a "loveable cuddly uwu cinnamon roll" or whatever. There are tons of other people who could've done a better, more true to the source, Stark.
Pierce Bronsnan, Matthew McConaughey, Ben Affleck, Jude Law, Mel Gibson, Matthew Fox, Johnny Depp, Brad Pitt, Russell Crowe, George Clooney, Colin Farrell, Clive Owen, unknowns at the time like Fassbender and Jon Hamm, and the list goes on. Tom Cruise would've been closer to the source too, with his signature mannerisms and demeanor, even though he's pretty short too, though a bit bigger than RDJ. If they made the movie in the 90s Nic Cage would've been great as well. Back in '08 you also had Timothy Olyphant, who would've been closer to the source. I'm still rooting for a lot of them for either Doom or Reed.
At the end of the day though, it's not so much RDJ's fault as the MCU's witing being very, very safe, so even with someone else we would've gotten the same result. The problem is that Stark stopped being a character, and RDJ kept playing himself, with his own humour, mannerisms and personality. But I will admit that I'm speaking from a hypothetical position of my "ideal" Iron Man movie. The point is that Stark's got more mean in him than translated, so I don't really see RDJ as a perfect portrayal.
It will probably be as "iconic" as Keaton's back in '89, departures aside, because of its importance, but it's just not the 1:1 to the comics people pretend. When I think of Tony I think of this All-American Oil Tycoon. RDJ's best role was Less Than Zero, where he played someone a whole lot less than a powerful and magnetic leader. RDJ's just a bit too "cute". Stark needs that edge to him. That maverick streak coupled with the sleek corporate executive look. You need that handsome, charismatic swagger with a hint of self-interest. For someone like, say, Reed Richards, you need someone who's warm, welcoming yet aloof and sometimes condescending even though he doesn't mean to. With Doom you'd need someone who puts out an aura of assurance, but beneath that he's a bomb that could go off at any moment and his charm is sometimes reptilian and demonic. Which reminds me, Julian McMahon could've been a pretty good Tony too, going off what I remember from the days of Nip/Tuck.