Allowing insurance companies to deny payments for covid related expense to the unvaccinated won't encourage them to get vaccinated. If the unvaccinated thought they had a real chance of hospitalization or death, then they would be vaccinated. The unvaccinated think covid is a hoax, or they won't catch covid and if they do catch covid, it will be just like the flu. The unvaccinated think the vaccine is a greater risk to their health than covid. Hospitalization and death from covid doesn't factor in for the unvaccinated, so paying for these costs don't factor in either. Additionally I don't want the insurance companies to have any more excuses to deny payment than they already have.
If you want to "weaponize" the insurance companies, you do it on premium side. Allow the insurance companies to ask for vaccination status and price discriminate based on vaccination status, just like smoking. Just 1% of the unvaccinated ending up with a $100K ICU visit this year would translate into roughly a $100/month extra in premiums for unvaccinated. Staring at $100+/month in cost would make the unvaccinated think twice about their stupid choice.