This is just a part of what is so ridiculous about their objections and reveals ignorance and a misunderstanding of law. The government isn't required to establish precedent here because it is already the law of the land.[1][2][3] That said, precedent has been very well established for a very long time.[4]
[1] https://uscode.house.gov/view.xhtml?path=/prelim@title50/cha...
[2] https://en.wikipedia.org/wiki/National_Emergencies_Act#Emerg...
[3] https://en.wikipedia.org/wiki/Public_Health_Service_Act
[4] https://en.wikipedia.org/wiki/List_of_national_emergencies_i...
Does it, though? Just because the government can mandate employees be vaccinated as a condition of continued employment, doesn't mean they can mandate employees be sterilized (for instance). No reasonable person would say the second follows from the first. Law isn't code.
Way to dodge the question. Also, I think you're missing the point. I don't think OP or most other anti vax mandate people think that the covid vaccine is a risky procedure, or that the public is better off on net for it. They're against it because it sets a precedent for government to mandate medical procedures.
>No one ever has any right to spread infection, not even libertarians.
You literally do, though. It's not against the law to get on a packed subway while you're sick as a dog, for instance.