Serious answer: because bandwidth is terrible. A transmitter the size of the LHC can only produce enough neutrinos (a few quadrillion per second) for a detector to receive a hundred per second or so. Accounting for noise, that means you can only achieve a few bytes per second at best, and again, that's with using the LHC to produce the neutrinos in the first place. With far less power you could instead use ultra-low frequency radio waves and still get better bandwidth.