TWOK doesn't need the shot because Khan died going for it, and you don't need to spit in his face with a token 'foiled again' bit from a cartoon.
I think Khan is seriously weakened in act III by a little too much mugging during the chase to Mutara anyway, and including yet another overreaction at the end would have been lowest common denominator thinking, which you've already got too much of elsewhere.
For that kind of payoff, you already have the 'here it comes' and the shields dropping and Khan's face going all hammy ... repeating it at the end would be like including a second 'dog farting' scene in Clint Eastwood's SUDDEN IMPACT, or Data -- after the 'ohshit' line -- muttering 'women drivers' after the saucer augers in during GENERATIONS. Piss in the audience's mouth, just don't pinch their noses shut at the same time.
By way of contrast, they went back and added a shot to the climax of TUC, with a three-frame cut of a dummy of Chang getting detonated during the torpedo assault that toasts the BOP. Production felt that was needed to tell the audience 'we got him' and for a film that operates largely on that kind of straightforward plotting, it does follow you need to dot Is and cross Ts in this fashion.