There's no reason it couldn't have been monitored remotely. As stated, it's just a fictional contrivance, arising from the fact that these things are designed based on what looks cool rather than what makes functional sense.
Yeah, I wasn't trying to justify it.
However, I think that the standard of what makes functional sense has to be applied with care. None of this stuff makes sense by the standards of the real world, which is why art designers have resorted to tropes such as the glowing/lightning look of the TMP intermix chamber.
But with respect to the art designers of STID, I applaud the choice of using the NIF for the new warp core. To my eye, the new core looks "more realistic" than any warp core ever shown in Star Trek.
Of course, the NIF didn't exist back in 1979. It's only been operating since 2009. Perhaps if it had been operating in 1979, it would have been the obvious choice to some, then, too.
What will it look like in 40 years? Dunno. Pre-transistor electronics still looked futuristic in the 1930's, but archaic by the 1970's.
But maybe that's irrelevant. Even if it doesn't succeed as looking like 23rd century technology to 23rd century eyes, the NIF has a better chance of looking like technology in our future, probably for at least the next few decades, than a totally made up glowing tube. That's still true even if (however unlikely it may be) actual 23rd century technology looks more like a glowing tube.