RDJ's manic personality worked well, but I could see a lot of other actors playing Tony Stark. Benedict Cumberbatch for one would have made a great Tony Stark too.
RDJ's Stark is just RDJ LARPing as a billionaire engineer. There's nothing in his potrayal that makes him embody Stark in a way that nobody else could. Comic Stark was a 6'0"+ buff guy who was butting heads with people because he had control issues, and would regularly have anger fits. RDJ played him as a careless playboy who gets more and more whipped as time goes on. RDJ just has a very "feminine" energy about him. I've said it before and I'll say it again, but RDJ is kinda like the effeminate Johnny Depp. Depp can wear dresses and makeup, but he has a masculine energy in his moves. He can play the drunken Sparrow, but then churn out a Donnie Brasco and John Dillinger. It's not that RDJ is a bad actor, but he just cannot sell the masculine archetype. And despite the memes, Comic Book Iron Man was basically a Male Power Fantasy that combined everything. He was James Bond but also Howard Hughes. He was rich, handsome, a man's man, he created marvels of engineering, he killed enemies of the state, he got the all the girls and so on and so forth. As time went on they gave him more and more hangups, but until RDJ started playing him, and the comics started immitating him, he was still as manly as Thor or Nick Fury. Now that's all gone and you have him on page crying to Carol Danvers about being intimidated by "strong women".
As for other actors, lots of them could've played him, really. Tom Cruise would've brought the action scenes, and a strong mania that'd suit a supergenius billionaire. Cruise also has that masculine energy I brought up earlier. Depp is obvious. I feel I should throw DiCapio in there too, alongside Colin Farrell. Brad Pitt is in the same vein and could've pulled it off. If we're talking a self-contained Trilogy, ala Raimi-Man, then someone like Pierce Brosnan would've been a great choice. Daniel Day-Lewis could've done a great character piece if you adapted the Stane Saga as a 3+ Hour Film. Clooney would've been nice. And yeah, someone like Cumberbatch could've done it as well. I've stuck to bigger names so far, but back in the day Matthew Foxx from LOST could've done it. Jim Caviezel is an underrated actor who I could see in the role. Timothy Olyphant and Sam Rockwell, who were in the running, would've been absolutely great as well. If we're going by "what ifs", then Jon Hamm could play the role in his sleep. Back when he was younger, Mel Gibson would've done a bang-up job. Heck, Russell Crowe too. Does anyone remember the rumors of Nic Cage being attached to the project? It would've been bonkers; in a good way. I'd have loved to have been in the timeline where Jackman did Stark instead of Wolverine. From [Current Day] I can safely say that Bradley Cooper would've done a great job. The list goes on and on...
So, honestly, there are a TON of people who could've played the role and done it a whole lot more faithfully. RDJ was at the right place at the right time, and because people have no experience with Stark as a character, they say that he was "born to play him". He's a good enough actor, and he's similar enough to one aspect of the character that he's managed to fool everyone. But he's not some incredible, one in a lifetime talent, and neither did he manage to portray a faithful 616 Stark. He's just okay. He's not Batman's Christian Bale, Affleck, or even Keaton. He's somewhere there near BatClooney. And it's honestly why it took me so long to buy an HT fig. The designs were okay, and the portayal was not to my taste. I caved in and POed the Endgame version because the suit reminds me of the Modular, it's the "last" fig, and I just want an IM on my shelf at this point. It's not like he'll ever leave his box...