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1) No healthcare is "free." You're either paying for it, paying for your insurance, or taxes are paying for your insurance.
2) Health insurance doesn't cover dental in the US, along with a huge amount of other countries. That's a separate insurance plan.
3) The reason dental is not covered so many places and is separate insurance is because the rate of dental trips for serious issues versus things like routine cleanings or an occasional filling are so low that it'd be a gigantic money sink for insurance companies/tax payers to include dental in health insurance. It's so far from essential the majority of the time, most dental things are easily preventable by just brushing your teeth regularly, so having people have regular trips to the dentist covered by any health insurance will drive the price of any insurance/taxes up so much to compensate.