midnight, since there is no "national medical system" in the US, the US government doesn't care what your insurance status is.
And since the States don't issue visas, they have no say in the matter.
In an emergency, most hospitals will take you in their ER (most, not all) and work out the details later, but if you are uninsured you can expect to get a bill. And private physicians will expect payment up front, cash or credit card, if you have no insurance.
Since there's no national medical plan and no coverage for visitors...it is up to you to decide if you gamble on not having your own medical coverage when you come here.
Unless you get arrested, in which case the medical care is free.
Not to derail the topic too far, but I'd have to say "yes and no."
I 100% agree that one of the major problems we have (and would apply to the OPs question) is that some pay 100X what others pay for the same service. You're right that if you're at the university hospital and you rack up a quarter million dollar bill and say you're poor they're apologize for sending you the bill (as happened to my neighbor). But if you're at another community hospital or private one without the same federal funding, they'll send the dogs of war (collections) after you.
The antibiotic for the bladder infection? Trust me, I've got the $4 list practically memorized. I also learned that the evil drug companies just took my favorite antibiotic (doxycycline) off the list going from $50 pharmacy cost for 500 pills to $2000 for 500 pills. On the other hand many docs are prescribing Fosfomycin for bladder infections because it's only one pill and 99.9% cure rate. It only costs $166.22 for that pill....
Bottom line. Our OP might stumble into my clinic with lots of federal funding and providers that know the $4 list, or he might go to a hospital/clinic that will order everything under the sun and charge the moon.
I also agree with Miniwaska that it's poor cruising etiquette to show up uninsured. There is a small part of me that is more forgiving of that because we don't even insure all of our own..... but it's still better etiquette to take us as we are, warts and all, and just man-up and pay for some insurance before making landfall.
Australia has some pretty severe and crazy quarantine restrictions on animals, but I wouldn't dream of showing up there with an unvaccinated cat hidden in my bilge. When I go off westward, the cat will have had her pokes, prods and tests because that's what my host has asked as a requirement that I stay as a guest in their country. America hasn't formally asked (read:required) for heath insurance, but it sure would be polite to show up with it.