And of course it would require explaining the distant supernova data showing simultaneous arrival of neutrinos and light. Well, both of the models of tachyons that I've seen say that their energy peaks at speeds approximately C. If the distant supernova neutrinos are highly energetic, that would explain it... the low population of low energy photons would be indistinguishable from background, having been smeared out so far in advance of the arrival of most of them that connecting them to the event would not be a natural inference.

The OPERA neutrinos are on the order of GeVs but the SN 1987A neutrinos were on the order of 1-10 MeV. So that doesn't work.