Honestly, dental insurance as as government single-payer system makes even more sense than regular health insurance as a single-payer system.

The real problem with dental insurance is that most dental procedures can be put off for a long time. People can go years with rotted falling out teeth. Foregoing dental work can cause you a lot of pain, but it's unlikely to actually kill you. This is much less the case with regular health insurance. If you get a cancer diagnosis, you need treatment now. You can't wait five years, save on the premiums, and then sign up for a plan for a single year and get all your cancer treatments done at once. With dentistry you can. This is why dental insurance tends to have annual maximums. Without them, people could forego dental insurance for years, wait until they have a whole bunch of dental work that needs doing, and then only pay for a dental plan long enough to get those treatments covered.

But with a single-payer dental system, that adverse selection problem disappears. With single payer, everyone has to pay for dental insurance every year via taxes. There's no saving up dental work for one expensive year once a decade.

Simply due to the nature of dental care, it's very difficult to make private insurance work as true insurance in the dental market.