Typically the normal modes of a system are whatever diagonalize its time evolution. Plane waves are a privileged basis for free particles because they diagonalize the free particle Hamiltonian. Unless time evolution commutes with annihilation (I have no idea how this could ever happen, but hey), coherent states are not normal modes.
>they are one possible choice of basis for the Hilbert space of states of the quantum electromagnetic field
This is true but it's looking at them from far too general of a perspective. Most of those bases don't diagonalize any interesting operator, much less the time evolution operator.
>they are one possible choice of basis for the Hilbert space of states of the quantum electromagnetic field
This is true but it's looking at them from far too general of a perspective. Most of those bases don't diagonalize any interesting operator, much less the time evolution operator.