If it were just the ship itself at stake, sure. But they've been flung a great distance away and need to rescue their captain and crew. If they jettison the core, then they're stuck at impulse and have no way back to the outpost. Besides, as I said, the dialogue indicates that Scotty had to rig the explosive bolts specially, so core ejection probably wasn't standard at the time (at least as envisioned in the episode). "Mudd's Women" established that "lithium" crystals were a key component of the power circuits, and "Elaan of Troyius" seemed to indicate that they were key to channeling the power from the matter/antimatter reactor. "The Alternative Factor" (which coined the name dilithium, the only thing from that misbegotten episode that's ever been referenced again) seemed to treat dilithium crystals as the ship's actual power source, but Charlene Masters's station was called the dilithium charging station in the script, suggesting that the slablike crystals there were some sort of storage batteries. TAS seemed to treat them similarly, as power sources that could be "depleted" and leave the ship powerless. TNG established that dilithium contains and regulates the actual matter-antimatter reaction -- that the dilithium atomic lattice in a powerful magnetic field serves as a series of magnetic microbottles that channel the matter and antimatter particles to collide and then contain and focus the energetic plasma that results (aka "warp plasma"). Without it, the reaction would probably be weaker because fewer collisions would occur, and it would also be less stable and controlled.