The NX has doors at the back of the ship to eject the warp core. The secondary hull was probably introduced to make this even safer following actual experience with Enterprise and Columbia.
Even with doors to eject the core, how did they not know that there weren't any unknown forms of radiation emanating from the core that would affect the crew. Sure they might've been testing Warp 1, 2 and 3 starships for 90 years, but Warp 5 was, from the sounds of it, an all-new engine that was very different from any of the other Terran warp cores, or even Vulcan. I'm reminded of Trip's face in "In A Mirror Darkly" and his line about his grandkids glowing in the dark, or even back in "Broken Bow" where Hoshi asks if it is safe to be stand near the warp core!
But even where I live there's a nuclear reactor about 30 minutes to the north of me. Even the town it's located "in", it is still about 15 minutes from the town center so that if anything does go wrong the main population of the town has a chance to leave (really, who puts a nuclear reactor in the middle of town?). And that's why I think the NX design was poor.