I think an important distinction should be made between dentistry and orthodontics. I believe that in many countries with public healthcare, dental coverage is pretty normal. What many governments don’t pay for is orthodontics (teeth straightening, braces, bite fixing, etc) and so most people go without it (eg memes about British people having crooked teeth).

In the USA, orthodontics is a huge industry. It’s all about having straight perfect teeth. I don’t know why it started, but the reason it’s stuck around is mostly aesthetics and inertia IMO. If everyone around you has straight teeth, you’ll feel left out if you have crooked teeth. It’s also a huge moneymaker for dentists themselves. I avoided dentists for several years because I got tired of them trying to sell me expensive aesthetic services, like whitening or special bite splints.

This. I think every culture has beauty standards, and some of them inspire a lot of people to do pretty drastic procedures. It's pretty mainstream in America to covet straight, gleaming white teeth.

I'm guessing there's some long history of orthodontics in USA that intersects with phrenology, marketing to people's low self-esteem, and piggy-backing on government and orgs' campaigns for dental health (extrapolating from medical necessity to aesthetics.)

Also I think there's a weird thing where parents are paying for braces for their kids. Notionally parents want their kids to be confident, but I also sense an undercurrent of social signalling of wealth and status, along the lines of putting solar panels on the north roof of the house if that's where the neighbors will see them.