I believe current Federal policy covers medical costs for COVID-19 testing and treatment. If we slightly adjust such policy such that only vaccinated or those allergic to ingredients or medically ineligible are covered, then I think perhaps it might be another incentive to get vaccinated. Of course, this should go into effect after the FDA makes the vaccines standard use not emergency use and perhaps 2-4 months after so.
Breakthrough cases would still be covered. People herd immunity is designed to protect would be covered.
People objecting to the vaccine for some conscientious reason would face getting the shot or a hospitalization that could bankrupt them. If they truly believe this is overblown nothingburger, then they can bankroll that bet.