How does between a teacher and student affect the teacher-student dynamic/relationship?

The legality and ethical side of it is very important to your question, you can't discount it with this question. It is the fact that we view it as immoral and it is illegal that changes the dynamic. A teacher is not going to be regarded as an authority figure if that happened by the pupil. The teacher will not have a professional attitude towards teaching a pupil either if that happened and will not be viewing them as present to learn but present to be in their company. That is why it is banned for even adults students and their teachers.