alt Hacker News20 times is a bit exaggerated.
I estimate mostly [3]. That's the whole discussion here.
If you wear braces, you have to visit very frequently. Half the kids in secondary school get them at some point. If you have cavities, it's usually several visits.
Granted, it does not come for free but it will set you back hundreds rather than thousands a year.
Are braces paid for by national insurance? If yes, I am surprised, as it is mostly cosmetic. That would be like national insurance paying for tooth whitening.