I've dealt with the cash side of the American system since I'm in a startup at Stanford and we can't get insurance until we draw salary. We've had a few folks in recruitment turn us down because they need coverage. Advantage large corporation.
There are very few unaffiliated care centers in the Bay Area, and most have prenegotiated fee structures that jack up the price for cash customers, since they are the minority here. We've tried to negotiate, but for large scale health situations (like surgery) you will not have any chance to ask for the anesthesiologists rates (both time and materials), the use of hospital facilities and materials. No joke, we got charged $500 for the hallway we were wheeled into before surgery, and nowhere did we get a preview of that cost. So perhaps you haven't experienced the awfulness of larger health issues.
I've been lucky enough (or perhaps unlucky) to use healthcare in various countries (Japan, Taiwan, New Zealand, Palau, various South Pacific islands). Japan was great care, small bill. Taiwan was not covered by insurance, but it cost the equivalent of $8 to remove a pencil eraser from our toddler's ear. Palau's health care didn't even have a thermometer when I came down with a jungle infection. Given a choice I'd take Japan and Taiwan over the US until the US has a true disclosure and competitive system.