Far fewer vaccinated people become very sick, or even get Covid at all. This is an established fact. SCOTUS has repeatedly upheld state vaccine mandates on public health grounds. The ABA has an online article about this called “Not Breaking News: Mandatory Vaccination Has Been Constitutional for Over a Century”. A federal mandate, however, is problematic on Tenth Amendment grounds.
A real libertarian does not believe that the public should pay medical costs. A real libertarian would also not force a private insurance company to cover someone’s costs even if the person is not vaccinated.