Mix voice is blend of chest voice and head voice. That means it is blend of mouth cavity and nasal cavity resonance. So what's the use of pharyngeal resonator or pharyngeal resonance?
I have to correct your obvious assumption that chest voice is associated with mouth cavity resonance, while head voice is associated with nasal cavity resonance. You always have a combination of all types of resonance, except for nasal resonance (including the nasal pharynx), which depends on the position of your soft palate. Without mouth resonance, you would not be able to produce most vowel and consonant sounds. Without pharyngial resonance, your voice would sound totally muffled. Different resonators cannot strictly be considered separate, but essentially, mouth resonance forms the lower part of the frequency spectrum, while pharyngial resonance affects much higher frequencies and is important for the characteristic timbre of each singer, for ring, clarity and air in the sound.