Yes. Everything about health insurance (which is what we're basically talking about) is a slippery slope.

Our health care system is unsustainable. And it's unsustainable because of one very simple reason: we want people to have absolute freedom and an absolute right to emergency care.

I don't think those two are compatible. I don't think they've ever been, but historically that contradiction has been papered over with others' money (either in the form of your insurance premiums or your tax dollars).

Cue present situation.

We have a scenario where there is a (1) free, (2) available, (3) well-tolerated, (4) effective preventative option in vaccines.

If someone chooses to remain unvaccinated, without medical reason, that is a pure personal choice.

And moreover, unlike in normal scenarios, their making that choice directly burdens everyone else.

Economically, through damage to normal economic functioning. And medically, through consuming limited hospital capacity.

These arguments could be made for other conditions (e.g. obesity), but in a much murkier and more tortured manner. COVID is crystal clear: if you can be vaccinated, and you choose not to be, you are imposing a greater burden on society.

Last I heard, the anti-vax crowd was big on personal responsibility. So why shouldn't individuals pay that debt of their own making?

I hear what you are saying but I can see this spiraling out of control. What happens when global warming and over population is considered to be a dire threat to the continued existence of human life? Do we allow hospitals to refuse services to women on their third child or men / women that refuse to be sterilized after the government approved x children. Seems far fetched but our definition of clear and present dangers can shift over time to fit the scenario something similar has already happened in China. I am very much not for allowing institutions to make those sort of decisions regarding the care provided to people as entities don't usually relinquish power once granted.

Edit: I am ok with triaging the vaccinated over the unvaccinated in a scenario with limited space as mentioned by another poster below.

What's the alternative?

You can't solve a resource limitation problem by mandating access.

And pretending to have free access, while in reality prioritizing the wealthy, is just a free market with ethical window dressing.