I'd object because it is going beyond the point where a character ceases to be the same character. Having Val-Zod on Earth 2 worked for me because he was a separate character, not the classic Superman with a different back story. Having another Elseworlds take where Superman was raised (and resembled) another ethnicity works because the whole point is to paly with a character's backstory. But for the main continuity (DCU prime universe comics, a movie series, a TX show) if you aren't sticking to the main backstory then you'd be better off calling your character Apollo, Icon, Hyperion, Supreme ….
It's the same as making a Bruce Wayne whose origin revolved around his criminal parents killing each other, a Peter Parker who uses an exo-skeleton based on the abilities of a spider, a Black Panther who has no high-tech Wakanda but rather a destitute African nation that has been fought over for thousands of years, … Any of these might be a great story playing off the standard tropes of the character or the basis for a new character who takes some of those tropes and uses them differently, but they wouldn't justify replacing the characters that have decades of sales behind them.