...There's quite a bit of tragicomic potential in a crush that goes unreciprocated because the object of desire requires any beau-hopeful to be nothing short of a superman! Subjecting poor young Chekov to this cruelty is just about the perfect choice.
There's also good drama in placing the still rather junior Chekov aboard the Reliant
: the TOS character there needs to be a meek victim to Khan, rather than a plausible challenger - and also something of an unquestioning lackey so that the very concept of Genesis does not launch him or her into ethical self-doubt and action immediately. Yes, Scotty might have had an ethical blind spot with a miracle of engineering, but Chekov is the likelier by-the-book, his-not-to-ask-why officer to do the Marcuses' bidding. And making Uhura a victim and then a traitor might have been unpalatable for a variety of reasons.
Swapping Chekov and Sulu would again have been an option, though. But, as pointed out, not an improvement in terms of "plot holes".