Maybe someone in Engineering was able to eject the core before the ship hit the planet. Granted that's the kind of thing that it would be nice to have seen, but...
Why would Khanone eject the core when he wants to destroy Starfleet Headquarters?
Funny is that also nobody aboard the Enterprise tried to eject the core/antimatter. Instead they were only concerned with restarting the core. If Kirk had failed, and the antimatter ignited, potentially millions of deaths.
Yeah, the writers indeed completely forget what kind of fuel the ships use, in all incarnations of Trek.