The drawback is the same in every case: The sheer amount of light that can pass through the optics of a spectrometer depends on its size. This in turn affects what signal-to-noise ratio can be realized.
These devices are certainly interesting, and performance is relative to requirements, so a novel application could make use of whatever sensitivity is made available by a particular device. But a tiny spectrometer isn't likely to be a drop-in replacement for a big one unless the big one is overkill for its application.
Still, I read these articles with interest, because my "size matters" rule is somewhat ad hoc, and there might be a factor that I'm overlooking.