Yes, yes he should.
For a storyline, at least.
As is the case with Batman and Robin, it should be a kid who has a back-story that mirrors Clark's, making him have that drive to mentor the kid. So for that I'd say Super-Robin ought to be an alien sent from a doomed world to be raised by humans in some regard. Probably not Kryptonian - but maybe a Daxamite. In that regard a more youthful version of Mon-El would work if he weren't from the Future. Obviously in some ways Supergirl fits this bill but is already too established and not as in need of mentoring. And thinking generationally anyway, Supergirl from 1960 falls more in line with the Dick Grayson generation of sidekicks, Conner obviously with the Tim Drake generation and Jon with the Damian generation so this would maybe be a 1980s-period flashback to when Superman had his own Jason Todd-era temporary sidekick? Back when everyone had the edgy sidekick.
So I think Matrix would be a good bet here if you were retconning, as a strange alien refugee who won't quite have as "easy" a time assimilating into Earth-culture as Clark had, what with being an extradimensional flamebeing Phoenix-Force scenario.
Then you know, just do a weird Phoenix Saga riff.