The US has the highest cost of healthcare primarily because nobody knows what healthcare costs. Even your doctor has no idea -- try asking sometime! I routinely point out to my primary care doctor that the medicine/test/whatever they're recommending is expensive and low-quality, and he looks at me like I'm an alien. Statistically, I am.
You're not wrong that you can get caught in a circle of hell after you get the bill, and that insurers are an opaque barrier to purchase decisions, but that's just saying the same thing a different way -- you have no ability to shop for what should be a commodity service.
> I have never heard of an insurance policy in the US that allows you to consume as much, and whatever type of healthcare that you want.
...and that's one of the few good things about our system, though I agree that the US implementation is maximally stupid. You should have to evaluate the cost and benefit of going to a (rare, expensive) specialist! While I agree that insurance companies suck, it's telling that the debate around this issue has devolved to indignation that someone should be acting to control costs by limiting the freedom to choose expensive things.