How can a phonon be localized? A meaningless concept? Yet Kittel...
We shall first determine the origin of phonon.
Lattice waves exist in crystal as lattice modes, and each mode corresponds to phonons of the same frequency and wavevector. My interpretation is that phonon is NOT the lattice mode itself. Rather, phonon is the quanta of interaction between its lattice mode and another object (electron, neutron, ......)
A non-quantized version of equations describing the energy and wavevector relations in lattice mode-electron (neutron....) interaction, partly corresponding to those in Appendix J of Kittel (8th Edition), could be taken as the origin of phonons. Indeed, the energy and wavevector relations of phonon can be derived WITHOUT application of second quantization.
Moreover, I would like to say that second quantization is "source of evils"; it is often introduced prematurely, as it is in some description of eletron-phonon interaction, which should be electron-lattice wave interaction actually.
This issue is far-reaching.
BTW, the same arguments would apply to interaction of light with other objects. What takes part in the interaction, photon or EM wave?