If you do not average dipole moments, you are calculating different thing than macroscopic polarization.I just can cite my former solid state theory teacher in that context: "Never average!
Jackson is not a solid state theorist but from particle physics, he does not know that."
In solid state theory you don't calculate the polarization from the moments of the atoms or molecules but you determine epsilon from e.g. linear response.
But as I understood it, the procedure Adler is describing is just a particular way to evaluate the macroscopic polarization, using the formalism of epsilon in Fourier domain. This epsilon then gives macroscopic polarization, whose meaning is exactly average bulk dipole moment. It may be hidden in the flood of formulae, but he uses density matrix to calculate averages.