Here is a review of the status of neutrinos . Currently there is no speculation of neutrino decays from higher masses to lower, and in the process. flavor violation.
However, lets assume that the heavier neutrinos can decay into the lightest neutrino very fast, so that only the lightest neutrino is measured in detectors.
If that were experimentally the case we would not have come up with the flavors for neutrinos and the standard model as it developed . For example we observe muon neutrinos to generate muons, this would never happen if the muon neutrino decayed fast.
Since the calculations of the standard model fit well within experimental errors the data, your hypothesis is ruled out, certainly for fast decays to the lowest neutrino it is completely excluded.