In the US, dentists and optometrists are separate from our health insurance system, and have their own insurance. Dental insurance usually covers cleaning every six months, and some percentage of the minimum possible correction for things that need work. For example, they may cover 50% of having the tooth pulled but 0% of putting in an implant, because the implant is considered cosmetic and not necessary work.

Anyway, it ends up being like you say, it's a largely out of pocket service that people shop around for.