The Neutrino: The Particle that Never Was

As I understand the origins of the neutrino, it all circled around the fact that beta particles ejected from nucleiwere observed to have a continuum of kinetic energies rather than a discrete quantum-driven value as observed for other nuclear processes (typically producing electromagnetic radiation, not charged particles). The competition between Meitner's group and Rutherford's group (specifically Charles Drummond Ellis) to explain this observation was a battle of physics titans. And it seems to me that they were ultimately content to call it a draw. Then along came Pauli, very down on his luck and desperate to gain attention with nothing to lose, who was willing to solve the conundrum by postulating a mass-less, charge-less particle that carries away kinetic energy. Since no one had a reasonable argument against it, the idea persisted (festered?) until ultimately Enrico Fermi dignified it by rationalizing it in a paper. Here is how I see the problem: The fundamental flaw in the thinking of everyone mentioned above was that they all assumed the nucleus to be a point mass and point charge. If you accept the nucleus as a sphere of homogeneous charge, you can explain the observations without a a neutrino.