So here's my general question: is that just a deflection to avoid talking about the permanent electric dipole moment of the electron? And, given that the general conclusion there is "the electric dipole moment is very small, if not zero", why isn't the very next step in the discussion consideration of induced dipoles in higher density plasmas? We know the polarizability is non-zero, where's that next approximation?
I am not sure I understand your question but a plasma is a kinetic gas governed by long-range forces (i.e., electromagnetic) that exhibits a collective behavior because of these long-range forces. Plasmas are also quasi-neutral, which means that the number of positive charges balances the negatives so that outside a Debye sphere the electric fields are shielded from those within.
Plasmas do have finite susceptibilities (e.g., see https://physics.stackexchange.com/a/547993/59023) and their index of refraction is not that of vacuum. In fact, the index of refraction for a plasma can get very complicated even for simple systems.
So to answer your question as to why we don't worry too much about each electron's dipole moment in a plasma, it's because the Coulomb potentials are dominating their dynamics. In extreme environments like near a pulsar or magnetar, the spin of the electrons and positrons actually do matter. In fact, the spin of fermions can matter greatly in relativistic plasmas under certain conditions (e.g., see discussion in answers to this question What is the correct relativistic distribution function?).
Is there any consideration of the intermolecular forces in a plasma?
Generally no because the dynamics are controlled by (and well predicted by) long-range electromagnetic forces.
