下頷is used in fancy writings in chinese, cause great writings, depending on the writer's style, usually incorporate archaic Chinese(文言文）or uses of older words to express a certain feel to the passage,
this is to either for sounding great and continuing the rythem and rhyme in how the words flow,
or literally just to seem fancy to feed self pride, it's like seeee I wrote something cool!
Or, for most cases, would be paying respect to the ancient Chinese culture and our cultural lineage, of where our words came from, it's like 飲水思源，ypu think about where the water comes from when you drink it, Chinese really pays attention to these details,
I mean the older folks were the ones who literally made these words so we respect our ancestor's hard work and creation.
Honestly, it really just depends on how you think, for why you are using the older version of 下巴 in the form of 下頷
下巴 is modern informal use in most passages amd conversations
下頷 is archaic but sounds really cool amd fancy, would be more formal, and also shows your respect and love for Chinese Culture
下頜 is the medical terminology where as the previous one sounds more culturally-informed for ancient Chinese wordings
Honestly I don't think many people even know the difference between the 3 since most just use the first version, the two other is just for language fanatics that wants to hone their vocabulary in the sense of sounding cool, building a feel to the passage, we do say that the passage you wrote can reflect who you are as a person, so the better you write the better one would imagine the writer to be as a person
I am so glad I knew Chinese as my mother tongue^^, because Chinese language is so wide and so deep at the same time, although it's still difficult for a native like me XD