> whether it's through taxpayer-funded healthcare or higher premiums for private insurance.
Insurance should insure your risk, and that's fairly independent of what other people are doing. (Of course, other people driving dangerously can endanger your health, and thus drive up your health insurance costs.)
What you have in mind is probably a consequence of forbidding insurance companies from charging people according to risk, and forcing them to charge people some average of a pool they are placed in?