Nobody's saying a massless neutrino would be incapable of carrying energy. Here's how I understand it: If a neutrino has no rest mass, there would be a variety

Nobody's saying a massless neutrino would be incapable of carrying energy. Here's how I understand it: If a neutrino has no rest mass, there would be a variety of ways in which the decay energy could be distributed, with some of it going to the electron and some of it going to the neutrino. So over many decays, the electron would be observed to travel at a range of possible speeds. You might see almost all of the energy going into the electron and almost none into the neutrino, or vice versa. But if some of the decay energy goes into the creation of a massive neutrino, that decreases the upper bound on how much energy is left to go into the electron. So by carefully measuring the extent range of energies of the decay products, you can hope to distinguish the massive and massless cases.