The new ships can dump their core, can�t they?

Yes. With the Next Generation and the ships of the 24th Century if there is a serious problem with the warp core, and you don�t think that you�re going to be able to solve that problem, the core can be ejected. It's sort of blown through a hatch at the bottom of the ship and with your impulse engines you can get away from it before it explodes in a fireball that would consume everything within several hundred kilometres.

In the original series, that was not an option. Gene had had nearly twenty years to think about how he would do Star Trek differently and he was a great one for discovering what features of the original ship that might have seemed somewhat dangerous or even reckless and how would we address that in the future.