The class G4BetaFermiFunction incorrectly calculates the Fermi function. A proper calculation of the Fermi function is provided by G4BetaDecayCorrections. A grep of the source tree in 9.6 and 10.2 beta reveals that G4BetaFermiFunction is not used in any other part of Geant4 (although the .hh is #included in G4NuclearDecayChannel.cc in the same module). So G4BetaFermiFunction should be removed.
You're right, this is now an obsolete class. It was kept around until G4BetaDecayCorrections was tested and used.