Dear OP,
I am glad you started this thread. Like you, I would typically start the first email with the more formal greeting, but then drop it on replies. I was looking through syllabi posted at a college that my D is considering and saw that a professor specifically stated that they were to be addresses formally/professionally in every email, including replies. My first reaction was that this was somewhat off-putting. But the responses here make it seem more just appropriate business etiquette. It makes sense to be more formal and then follow the professor’s lead on follow-up emails.
I do think this has something to do with proper business correspondence format, but I wonder it it might also have something to do with how someone views email. If you view it as ongoing correspondence, the formal format makes sense. If, like me, you tend to view an ongoing email (replies back and forth) as a conversation, then the greetings seem awkward, since you would certainly not use them if you were speaking face to face.