I regards this as a counter-example of v_p v_g=c^2,although v_p v=c^2 is universal.That is to say, the group velocity vg is not always equal to V. It can be applied to explain why those experiments of superluminal group velocities vg>c are not really faster than light v>c.
But in optics and electromagnetism, v_p v=c^2. is still valid to a field(photons) in vacuum. On the other hand, the photon can be described in relativistic mechanics as a special case of V=c and m_0=0
E=hw and p=hk is of course tenable to photons otherwise the Compton effect, photoelectric effect, blackbody radiation and others cannot be interpreted. In history, these two relations are concluded from experiments to massless photons and then de Broglie extended to massive matter...
The study to vp in conductors is based on first principle(Maxwell's equations) and has nothing to do with parameters in circuit theory such as voltage,inductance and capacitance. For example, J.D.Jackson's <Classical Electrodynamics> and D.J.Griffiths's <Introduction to Electrodynamics>...
In <Engineering Electromagnetics> written by W.H.Hayt and J.A.Buck( 6th edition,McGraw-Hill,p372), the phase velocity vp of electromagnetic waves in copper at 60Hz (commercial electric power) is 3.2m/s. Substituting the value into vpv = c2 of de Broglie theory, v=108c should be much faster...