There are for profit and non profit hospitals. The non profit and for profit hospitals expect patients to pay their bills and will take anyone to collections to do so.
Medical issues are the leading cause of bankruptcy in the United States.
If you start your own business ... or work for the many companies who do not provide insurance and you have an accident and a few days in ICI and and another week as inpatient will land you about a 100,000 bill. There is no "public" hospital to arrive without insurance for 'people who are not insured".
The NP will will go after you until you pay your last penny and then the rest of your care will spread to others through astronomical cost.
It is irresponsible to not have at least catastrophic insurance and even more irresponsible that out country has a system that make sit almost impossible for many to have insurance or for some ... to be negligent simply because of EMTALA and other laws in which catastrophic care is given and others simply pay for it.
Ridiculous ... Do you realize how expensive "public" hospitals would be in very region that offered "free" care as you have imagined. Why not HCR ... simply organizing a system with a choice of private or public that citizens can afford. A public option payer would have offered competition to a monopoly market.