Iron Man was right in Avengers: Infinity War, Marvel Studios pit its biggest heroes against each other highlighting not only the difference in their perspectives but also experiences. The Joe and Anthony Russo film from 2019 didn't explicitly state a winner, but subsequent events suggest that ultimately, Tony Stark's stance was correct.
By the time Civil War took place, the Avengers have been operating for a few years already. There was already a roster shuffle from the original lineup that fought Loki in the Battle of New York in the introduction of the Sokovia Accords. It's a deal that would put the heroes under United Nation's jurisdictions. Interestingly, Steve Rogers was against the idea, while Tony Stark was for it.
Civil War spent time with the heroes making a case for what they think they should do, and eventually, each one chose which side they were for. Captain America argued the safest hands were still their own, which made sense, considering what he'd just experienced in Captain America: The Winter Soldier. Meanwhile, Iron Man countered that without limitations, they're no better than the bad guys. Unfortunately, the Avengers couldn't find a middle ground so they clashed.
Given how both sides laid out their choices, it's ittedly difficult to decide which one was for the better, but with what's currently known about MCU Phase 4, it's getting increasingly clear that Tony Stark' approach was right. His plan wasn't simply to surrender their agency and be puppets to the government. As he explained, in their initial huddle, it's best for them to adhere to the protocols and work their way into gaining their full autonomy back. That way, they can effectively resolve the issue then and there instead of prolonging it by stubbornly refusing it. It's been several years since the events of Captain America: Civil War; its ramifications may have been sidelined by a bigger problem in Thanos, but now, the remaining heroes have to deal with the belated consequences of their choices.
This issue is most prevalent in The Falcon and the Winter Soldier with the government eventually taking the shield from Sam, effectively WandaVision, she might still be deemed a threat.
Aside from the MCU Phase 4 ramifications of Captain America: Civil War, the subsequent events of Avengers: Infinity War was also proof Iron Man was right. Granted that Captain America did have a very valid point during the debacle, but had they made concessions, they would've stayed intact and more prepared when Thanos attacked. Tony's speech in Avengers: Endgame highlighted this, and while there's no guarantee if they would've won if they stayed together, it's certain they would've done a much better job at protecting Earth as a unit than separated.