I agree and disagree.
I don't think you can have a black CLARK KENT, because a black man with incredible power would inevitably be feared and hated by a decent chunk of the American populace (citation: our previous President), would have a very different experience growing up, and would provoke very different discussions about power and its proper use. He's no longer a recognizable character, any more than if he was a woman, or gay.
But those discussions are worth having, and there's no reason you can use Superman to have them. President Superman was black. The Superman in Gods and Monsters was latino. These weren't Clark Kent, but they were Superman, and their race impacted on them just as much as Clark being a corn-fed white Kansas farmer's kid impacts on him.
There are other characters where this is the case. You can absolutely have a latino Batman, but Bruce Wayne is a fundamentally white character. An asian Captain America could work fine, but an asian Steve Rogers would not be recognisable.
That's not always the case, though. Wonder Woman (Diana) being black wouldn't fundamentally change her story or character at all. Spider-Man (Peter Parker) could be black without more than secondary changes, which is part of why Miles fell flat in the comics. Other than Angel, any of the X-Men could be pretty much any race without a hitch. Similarly, Bruce Wayne is a pretty fundamentally straight character, as are Logan or Hal Jordan, but you could write a gay version of Steve Rogers or Peter Parker without much of a hitch.
This is why people who flipped their shit about Falcon being Cap annoyed me, moreso when they complained he was dealing with what it'd be like to be Captain America as a black man. That's how you do it RIGHT, brainlets, as compared to Spider-Gwen just dropping in a black lesbian WWII-era Captain America for its setting like that makes a goddamn bit of sense or would produce even a remotely similar character.