The idea that having insurance changes the cost is sort of a misdirection. There's a chance my plan doesn't cover some or all of things that will be billed. So there is always a risk of non-payment or partial payment. Yes, they sometimes do pre-approvals for specific procedures but that doesn't always translate to proper billing/coding that gets covered.
The vast majority of healthcare are not ER visits which means people have a chance to review and accept the responsibility of payment. But that would also mean they would know what the hell they would be charged. There's no good reason for a hospital to say "oh you don't have insurance so we're going to basically mark your bill up 3x just to be safe. Marking the bill up 3x, for example, doesn't change the fact that they are really only seeking 1x so the people who can afford to pay 3x are legally required to do so because for some reason this is viewed as a legit practice and not fraud. And the people that can't settle for something less than 3x, usually much less. Maybe 1x...in which case the providers gets what they were after anyway and just indicates further that this is a sort of fraud and extortion.
This is incorrect. It's absolutely the other way around.
You're not referring to the common practice of bill inflation are you? For example, a tree falls onto your house and the damage is covered by insurance but the contractor knows insurance is paying for it so he jacks up the price once he finds out what you are getting from the insurance company (they tend to ask so that they can "plan" accordingly to stay within budget, but really they just want to make sure to capture the entire insurance check). This is 100% illegal but very hard to prove, hence it goes largely unenforced. With healthcare it's well-documented but still unenforced.
If you are referring to something else I would be very interested to know what else operates in such a manner.
Because in the US model the insurances negotiate with the hospitals what they pay, and you will almost always be given a number that is way higher than the highest insurance amount - as when you pay yourself the hospital has a high risk of never being able to (even partially) collect the bill. Also, it must be higher than the highest insurance amount so that if you were an undercover agent of your insurance you would still believe you pay less than others.