It's the same room they tested the completely unknown device from DS9, which did malfunction and happened to shoot out a beam of energy out of one end. Instead of going into the core it shot out the other side and gave a crewmate the ability to dream. Which they proceeded to do the same thing again but for longer.
Warp core can have shielding around it but typically doesn't. There have been threats in the past from people firing at the warp core. A containment field can be raised (and iirc there was one raised in this scene) but it's not always on. Would no need to be in an area as critical as main engineering. Only people with access to the area are people who wouldn't typically fuck with it. Having a continuous forcefield would be a drain on ship energy systems and might even impact crew morale to an extent.