It's a really unfortunate historical accident, especially in the US.

Dentistry evolved relatively late compared to regular medicine, and early oral procedures were mostly tooth extractions, which ended up being predominantly done by barbers, who would also do surgery (!). These procedures were often considered crude and beneath that of a trained doctor, and they were generally performed by self-trained practitioners. There were several attempts in the 1800s to integrate dentistry into mainstream medicine, but they failed, both because the doctors of the time didn't think of dentistry as being a real science, but also because, as dentistry started to legitimize itself, the dentists themselves preferred being separate.

For some reason the same separation also evolved in the U.K., but it's more integrated in other countries. For example, basic dental coverage is part of national healthcare in Germany and Japan. In the U.S., dentists have their own schools and licensing boards and so on, which isn't the case in the rest of the world, where dentistry is usually accepted as a regular branch of medicine and taught at the same universities.

I literally remember one of my elderly relatives pulling out a tooth at home with a thread tied around a door handle as if this was nothing special. DIY all the way! Early 1990s, former Soviet Union rural-or-so area.

As of today, we have moved to a different situation where dental care in that same country is ample, but the price lists are rarely transparent, making many not-so-well-off people avoid going to dentists altogether.

The health insurance system gives something like 60€ yearly to an adult for fixing teeth. Dental care for children up to 19yo is for free, though, which is great.

It's not just in the US. In all the EU countries I lived it was also excluded from standard health insurance and government programs except in cases of acute damage.