Yeah...People are severely over-estimating the cost of braces and dental work in general. It ain't cheap, but they're relatively cheap in comparison to hair transplants and all that garbage. Plus you can always just get dentures if it all goes to hell. The thing that makes teeth cost a lot is when you get them whitened like a movie-star. That will kill your wallet, but that wasn't the OP's idea.
If you have insurance w/ dental, then all the teeth problems become even cheaper. A $25 co-pay twice a year, plus the occasional filling. Not a problem.
Let's assume you have super screwed up teeth though. There's basically only two things you need: fillings (or crowns) and braces. If you don't have any teeth, get fakes or dentures. Based on this link the fillings will cost you about ~$100 each. Crowns are ~$300 each, and a root canal is about ~$200. The average human has 30 teeth, so if you had to get a filling in each one that's $3000 without insurance. Braces cost around $5000, but let's say $7000 after including a bunch of check-ups. So if you have atrocious teeth today, you can get to "problem-free" teeth with less than $10000. That's a hell of deal. Again, this is all without insurance.
Granted none of this accounts for if you have really really really bad teeth. But that's not common at all. Teeth are pretty resilient, and it takes a lot of poor hygiene or drug use to really screw them up to the point of no return. Again though, just get dentures for ~$1000.
Now for hair, that's expensive as hell. You're looking at $5000 - $15000 for a hair replacement that may not even work. It's also never going to be covered by your insurance.
Moral of the story? Yeah teeth can get pretty messed up and hurt bad, but dentists are good at their job and teeth are sort of "figured out". They're cheap to replace and fix - even cheaper to keep clean and healthy. Hair is much more variable and random.
Fillings are per surface, not per tooth. So that's five per tooth.