This is exactly my original point. Why reuse Khan and turn him into someone completely different than what we know?
TWoK already did that. While I loved that movie, the Khan from TWoK was barely recognizable as the same character from Space Seed
(except, of course, for the obvious: that they had the same name and were played by the same guy).
Honestly, there was really not much of the "Eugenic Superman bred to lead the world" aspect of Space Seed
-- which was the most important plot point of that episode -- that was used in TWoK. Instead, they took the character of Khan and turned him into a broken man who has gone mad with revenge.