I'm glad that didn't happen, because it would have been fanwankingly stupid. None of the casual moviegoing audience would have known that it was Khan's ship (and if they did, they probably wouldn't have cared)
I don't see the problem there. None of the casual moviegoing audience knew who that guy in the final scene of The Avengers was, so what? By that logic you would have to drop all Star Trek references whatsoever and make it a standalone movie with no backstory at all. But that wouldn't be Star Trek, would it?