It seems to me only natural to write a note to any teacher you connected with who gave you enough of their time and teaching that you decided to apply for their school and studio. That’s just a polite acknowledgement of the human interaction. Beyond that, it’s a small world, and you never know when you’ll see that person again; summer festival, graduate school, master class, competition… it’s important for students to know how to engage on a professional level in the real world. And as the expectations of courtesy are lowered in this crazy world, they may even stand out!