STDs spread. It's not just the one patient who benefits, is it? Fantasize about people not spreading STDs all you want, it came from somewhere and can go further. Public health isn't just the one person.
You're making the case that the market would have the incentive to provide these things because the insurance company would rather pay for an expensive test than have a larger number of claims if the disease spreads.
The existing law has a massive defect that prevents any of that sort of thing from happening right now.
We capped insurance company profits as a percentage of claims, so the only way they can make more money is by paying out more and bigger claims. We basically banned them from having any incentive to lower costs because now lower costs mean lower profits instead of higher ones.
But that's a flaw in the existing system, not a flaw in the general concept.
> They'd be ripping a new one in the meat industry to forestall antibiotic resistance, for example.
There are already various state and federal laws restricting the use of antibiotics in livestock. But in general what leverage does an insurance company have over the meat industry?
Same leverage they have over any of their customers. Raise cost of premiums or refuse to issue policy.