The thing is, bad and expensive health issues can literally come upon you over night. You can get hit by a vehicle or get beaten up with no perpetrator to be held accountable, you can develop an aneurysm, get food poisoning, get pregnant unexpectedly (with all the risk that comes with, including healthcare not being accessible because of anti-abortion BS), or you can simply fall over a step in your own house.
There has to be SOME point where the constant muggings aren't worth it vs the risk, otherwise they would simply demand all our money, knowing we won't say no with our life on the line.
Aneurin Bevan
What I think we have now is the most non-market like sector of the economy, with 1/3 of all citizens already receiving government funded healthcare.
Realistically catastrophic revolving temporary insurance plus managing what you can in Mexico, plus occasionally paying out of pocket would mitigate the vast majority of yours risks while keeping expense relatively low.
They'll only treat you until you're stabilized, though. They won't give you chemo or routine care. If you need to be admitted you're also not covered by the EMTALA.
All emergency medicine, not just that triggered by the EMTALA, is 5-6% of all healthcare spending in the US, so while it contributes, it's not collapsing the healthcare system.
The real problems with it are that it's an unfunded mandate by Congress, just adding to the financial tangling of the healthcare system, and that it's way too often used to treat things that could have been much more cheaply treated in a clinic, but then there are no clinics nearby that take Medicaid and are actually open, so instead, like with so much of our health care system, we choose to solve it the stupid way instead.