This allows Khan to remember Chekov without him having to hide somewhere on the ship for the first year of the show.
...But you seem to be counting by stardate, which means Chekov is already a bridge officer by the time of "Space Seed", having made his debut earlier on in "Catspaw".
Well, at least it completely and totally avoids the whole "people with yellow hair and pale skins are somehow superior" nonsense.
But just because it's nonsense is no reason to avoid it - indeed, it being nonsense is why it's so darn popular in entertainment. "Nazi" isn't pronounced "nutsy" for nothing.
That is, if somebody on Ceti Alpha V decided that people with white hair and pale skin (say, Khan, which his already white hair and non-negroid complexion) were superior, he'd certainly act on it! Now that the desperate flight with some eighty competitors was over, and compromises could be forgotten, the elimination game between the supermen could finally begin. In the end, there can be only one (phenotype)...
As for the nuances of dialogue, fitting your model in isn't all that impossible in the end. Khan does say Kirk marooned him and the others "on the barren sand heap" (contradicted by facts of marooning in "Space Seed"), and "never bothered to check on their progress" (made doubtful by the 15 years reference if taken literally). Might well be Kirk marooned Khan twice, then: first on the harsh but fertile Ceti Alpha V, then again on the barren sand heap Ceti Alpha V (by visiting, seeing that things were bad, and nevertheless leaving). And then
he failed to check on how they were doing.
Kirk would probably have done all that on his own time, though, without bringing his starship along. The place isn't all that
far out in the sticks, and Kirk has access to various private or commercial starcraft when the UFP doesn't declare an inconvenient quarantine to hinder him. Or then he can operate small Starfleet craft of sufficient range, like the various TAS designs, and file a false flight plan.