Great. Those formulae are derived from statistical representation of huge number of particles, eg electrons modelled as a nearly-free gas of fermions obeying Fe

Great. Those formulae are derived from statistical representation of huge number of particles, eg electrons modelled as a nearly-free gas of fermions obeying Fermi-Dirac statistics. And so too would anything making use of PN junctions, band gaps, especially when considering temperature dependence. I think you can agree now that your original observation of statistics as "glorified curve fitting" as a bit naive.