Actual details vary by state, but this is how CA does it: https://dhs.saccounty.net/PUB/Pages/Communicable-Disease-Con...
This seems reasonable to me. I don't think the right to privacy extends as far as the right to secretly give people diseases, especially ones that cause permanent damage and possible death.
You seemed like were balancing things, then you ruined it by speaking out both sides of your mouth with that.
What you've effectively endorsed is "You have the right to privacy/secrecy as long as I don't care to look."
Everyone already has that. The entire point of a right to privacy/secrecy is to strictly corral what can be looked at/for/and how even when the People come looking.
You just threw out the entire point of the 4th Amendment there. No need for warrants, or to strictly define what the public interest is. Just define anything you're looking at as the public interest and have a party. Hell, you even threw out a workable implementation avenue of specifying that this carve out from the 4th only applies to legal fictions, which wouldsolve half your issues right there. Anything illegal would have to be done by a particular person or cohort of people outside the confines of legal fictions, meaning evidence lines should very clearly lead to individual parties; or at least until people stopped using corporate entities to do sketchy things plausibly like they do now.
This is obviously a tricky and subtle distinction, so yes, one absolutely needs the sort of power-restricting and rights-balancing apparatus that getting a warrant is an example of.
For me, right to privacy declines with impact to others. What you're doing alone in your house? Don't care. Between consenting adults? I almost don't care, except when public health matters (e.g., STDs, or COVID contact tracing). but the more we move toward public impact, the more I think there's a public right to know.
Another way to look at it is that people have a right to privacy, but not secrecy. Me lending my brother some money is reasonably seen as private. Me giving the same amount of money to a legislator as a bribe is something I might want to keep secret, but given the public impact, can't really be called private.