Likewise, while it's entirely possible a black Steve Rogers might've been subjected to horrifying medical experimentation in the '40s, he still would've been serving in a segregated Army, and kept even further away from the front lines than he was as a USO act. Black enlistees had a three-year waiting period before they could begin combat training, and the Tuskegee Airmen weren't even deployed until 1944.
A black Steve Rogers or Tony Stark would be as different as a white T'Challa would be (which, as some wags have pointed out, is basically just "Thor"). That's not necessarily a reason those characters couldn't be reimagined as black, though (it's not like there's a shortage of popular white headlining superheroes). Captain America would probably work better, you could swap in the segregation thing for the PR-monkey thing in the film, though I have trouble thinking of how African-American Tony Stark wouldn't end up being a lot more like Whiplash (son of a brilliant inventor whose work and legacy was stolen by others while he was erased), or maybe just one-man Wakanda, creating all these technological wonders that are ignored by others either because they can't believe they were made by someone like him, or hidden because other people would take the credit.