Then why doesn't a country with a nationalized health care system do it? There are incentives in other countries that would encourage this, if it were possible.
Regardless of the type of healthcare (nationalized, private, etc..) the dental health industry is still getting paid, the only diffference is who is doing it. The original statement was that a breakthrough in preventive medicine will destroy a large portion of the bread and butter of the dental health industry, which will lead to it being only a fraction of what it is today. Industries fight tooth and nail to keep growing. Guess what they do when their existence is threatened.
No, one difference is who is doing it, another one is the sums being payed. That's why the dental industry in countries with national health care fight to stay out of the general health system. The lucrative compensation of the practitioners lead people to want to go specifically for that. If it were part of national health care it would cease to be sure path to accumulating loads of money, the incentive to become a dentist as well as the power of current practitioner will be similar to that of family doctors or orthopedic specialist. Spoiler alert: in countries with national health care their status is higher then the status of teachers in national school systems, but not by much.
Why defer to a baseless "probably" when you can easily check what is known about the past? Wikipedia doesn't put the blame on refined sugar but rather point to farming as to what correlated with dental issues. Are you familiar with the barber's pole? that's the sign for the location where our ancestors went to be relived from owning teeth.