If my kid did this, the last thing I'd ever do is make him remove them. I'd want them to stay on as long as possible so (1) he could experience all the difficulties in eating, talking, etc. that he could in the meantime, and (2) I could get some good pics to share with his spouse, and with his college and professional friends, when the time came.
This is a temporary thing. Still seems a waste of $200. And not much different than getting a grill (ask them if they’d rather get some bling, or is that NO LONGER COOL).
Take pictures. They’ll never live them down.
But as to the dentist, it probably helps get kids to WANT to get into the dentist (where he can also give them an annual exam, etc.).