It's because Ricardo Montalban made the character iconic and strangely timeless.
Replacing the Enterprise crew is fine because we've watched them age, so saying that these are the "younger versions" is fine since we're 40 years removed from the actual younger versions (who, in all honesty, haven't quite stood the test of time).
Montalban did something with Khan. He transcended the usual Baddie of the Week and created this weird villain who possessed more gravitas than anybody he shared a scene with. This was such a stand-out performance that, yes, it essentially became the foundation for what we could arguably call an early reboot of the movie franchise.
His return was a very different and very powerful Khan. He stole the entire fucking movie... He killed Spock!
Replacing Khan would be as painful as replacing Doc Brown and Marty from Back to the Future, rebooting Die Hard with a new John McClane, redoing Alien without Sigourney. Can you picture any of that? Sacrilege!
Gary Mitchell is a great character... But, come on, that's a shit-ass clunky episode with styrofoam rocks, over the top acting, and it just screams "I'm from the 1960's!!!"
Space Seed has clunky moments, and also dates itself horribly... But don't you think that early Khan was engaging and unique? They even took the daring step of portraying him as not entirely evil... There are so many complicated turns that episode takes. Spock's admiration of Khan, Kirk's decision to be merciful, Khan's acceptance of defeat and punishment. All of that played against these moments of stalking terror as Khan takes the ship.
So I went on Youtube to look for some of those great scenes where Khan defends himself (and tries to explain that he wasn't such a bad dictator) and, instead, I found this: