The next time you watch Generations and get to the line where he says "We're five minutes from a warp core breach, there's nothing I can do" shout "eject the core" as many times as you can before the ship blows up. Actually, stop after five times, because it's just annoying.
You can't tell me Galaxy Class ships didn't have a Warp Core Eject function... or can you?
Could also be the type of damage sustained to the core precluded the possibility of a safe ejection.
I maintain that the warp-core has two independent cooling system. One for the "containment field" equipment and one for the reaction byproduct heat. This would cool the crystal, the crystal frame and carry waste heat to a conversion/disposal process.
The traditional loss of coolant would allow for an ejection as there would be sufficient coolant reserve within the core to provide a margin of time sufficient to prepare the core for ejection.
The second one, the one we see in Generations... is a failure of the containment system cooling equipment. Say they use some kind of "subspace magnetic field" to contain the reaction. Those generators and coils need to be kept cool, so they have a separate cooling system.
Failure of those systems would cause a gradual decay of the containment field as the coils heat up and stop generating.
I base this on the line "the breach is accelerating" in the movie... as the coolant inventory decreases the coils would heat up faster and lose strength faster.
The core was already unstable due to damage, LaForge wanted permission to shut it down because the "magnetic interlocks" were unstable... Trying to eject it would have caused the already unstable core to breach.
Laforge... being the highly trained professional... knew this and instead switched from trying to save the ship to getting the crew off.
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To me ejection never made sense anyway... you have a damaged container of volatile nuclear nuclear reactions running at full power... LETS DISCONNECT IT FROM THE SUPPORT EQUIPMENT AND SHOVE IT OUT A HOLE AT SPEED! Hm no. Does nothing for me.
A more "real" approach would be a positive shutdown mode like REAL nuclear reactors have. Push the red button and the reactor SCRAMs.
However, the point was to destroy the ship. In order to continue the drama have the core break down, and LaForge shuts it down. Moments later they find that the damage extends to the antimatter storage pod systems and there isn't sufficient time to eject the pods.