It isn't mandatory health insurance that makes it more expensive: I have taxpayer funded insurance, which basically makes it mandatory for most (some folks don't qualify if you are a certain category of immigrant, but you still have to have it). There is a private option if you want to pay extra.
... And the system is more efficient because of standardization and pooling money together.
The US system doesn't have much of any standardization, and in general has a lot more facilities than it might otherwise need - plus things like some of the government provided insurance not paying enough and not having the ability to act like public insurances. These all make it more expensive. Heck, even standardizing insurance coding would help.
It is cruel to expect folks to take out a loan for medical emergencies. In some places, you die if you can't pay. It isn't like health is completely under your control: Type I diabetics couldn't prevent it (for example). Many cancers can't be avoided. And so on.
Negotiating with medical facilities is a pipe dream. There are many cases where you simply don't have the choice (emergency) nor the mental space to do it (for example, do you know how to judge what facilities are better for a gall bladdar removal surgery? How about where to get cancer treatment? How does one judge any of that?)
Does care insurance cause you to drive fast? Seriously? Isn't that more cultural than whether or not you have insurance?