I mean, the numbers certainly show that unvaccinated people wind up in the hospital at a much higher rate than vaccinated people and being in the hospital by nature costs a lot more than not being in the hospital. I don't think that's really in dispute and I can assure you that insurance companies have actuaries and epidemiologists who have run the numbers many times. So, if it's not the case, they won't raise premiums for the unvaccinated, they will just raise premiums for all of us spreading the cost across all of society.
How you react to that is a different question. But, I do think it's the case that insurance companies always use "risk" of higher medical costs and the major factor in setting insurance rates. I mean, the whole point of insurance is the spread the "risk" of health care costs over a larger portion of society in order to theoretically keep the costs down. That has not been the result for a lot of reasons (mostly because health insurance is tied to employment and the free market doesn't really work for a service for which there is basically an infinite demand no matter the cost), but that is why we do it and how they set premiums. Whether we should be using private insurance to take care of health care needs is another discussion entirely. But, if that is how we are going to do it, the result will be higher premiums for people at higher risks for higher health care costs.
It's not about "calling out" people who are unvaccinated, or calling out smokers or obese people for that matter. It's just a simple fact of the insurance industry that higher risk equals higher cost.
And smokers and obese people are already paying extra premiums for their increased risk. Not sure why unvaccinated people should be any different.