Actually, any authority not explicitly given to the government in the US Constitution is implicitly a right. See the Tenth Amendment. Also, wouldn't those fall under the right of privacy used to justify abortions or the right to due process protected by the Fourth and Fourteenth Amendments?

Possibly yes, in principle. If it is non-punitive, like most of the licenses in existence. For this a few points will need to be satisfied though, which, in my opinion are not, at present.

- It needs to be shown that significant difference exists in the degree of risk/harm reduction between "licensed" and "unlicensed". That reduction must be measured and quantified or qualified beyond reasonable doubt. The threshold of significance also must be socially agreed upon.

- Likewise, the very risk/harm to be reduced needs to be shown as being worth an essentially society-divisive measure. Again, the agreement needs to be reached on where exactly the the tolerance threshold is. Such that it is clear why the same mechanism is/was not applied to other things. Like, why we don't enforce it for seasonal flu, why we don't have blanket 10km/hr speed limit, and why when throwing a BBQ for friends one must not apply for permission and provide proof of recent "food handling safety" certificate.

- At the same time the requirement must be universal, no exception on any grounds, medical or not. Just like blind or mentally deficient person is unable to get PPL or DL, under any circumstances, even though the disability is not due to their choice.

- The latter must be recognized and "unlicensed" people must not be shamed or vilified. Conversely, creation of the alternative infrastructure must be encouraged, in order to bring these people back into society. Just like we do for people with other disabilities.

Otherwise it is just petty punitive crap. Like in Victoria, where "unlicensed" aren't allowed into KMart, but can run wild in Coles across the floor. Or not allowed into restaurant but happy to mingle in the food court. And honestly, so many measures for the last two years were just hostile and punitive and useless otherwise, it is not surprising that they tend to be rejected as a package, even when you can, arguably, sift one or two reasonable things from it.

I like to think of the covid vaccine as a potentially forced evolution of humanity, of which a certain subset of its constituents favor reducing the rights of those whom refuse it - a group that they were apart of not so long before.