It was kicked around a few years ago as a way to get a jump on competitors in high-frequency trading:

https://www.math.columbia.edu/~woit/wordpress/?p=4646

It's not impossible, but it's kind of absurd. Neutrinos are insanely hard to detect. You need immense detectors, and even you get only a ludicrously tiny fraction of the neutrinos passing through. You'd have to modulate it by turning on and off an immense nuclear power plant, so despite shaving off milliseconds of latency you still wouldn't be able to communicate fast.

There's no reason to expect any of that to become more practical any time soon. Neutrinos are too small, too fast, and too devoid of interaction to manipulate easily.