And, true to form, with other types of insurance I pay "routine" types of costs myself; for example, I have auto insurance, but I don't expect it to pay for a tank of gas or an oil change. I pay those myself, and have the insurance available for things like accidents, which are unpredictable and far too expensive for me to pay for all in one go.
And yet... health insurance tends overwhelmingly to pay for predictable routine treatments (yearly checkups, for example) while balking at paying for precisely the sorts of large unpredictable costs it's meant to help manage. How'd we end up with that system?
Second of all, those plans that do cover routine care generally do so under the theory that, by paying a small amount of money for routine care, they're avoiding paying much more down the road when the cheap problems that would have been caught at a routine physical turn into big, expensive problems.
Anyway, I don't think the average person has the option of venue-shopping between two countries, one in which he has nationalised health insurance, according to preference.
Example: I am covered under national insurance for dentistry in Japan, but Japanese dentistry is a nightmare (in no small part due to the fact that it is covered by national insurance), so I get it done when I go back to the US to visit family. Since I have no American insurance, I pay cash. And its so easy. After spending literally 15 minutes explaining to my dentist's office that I would be paying cash (and was not unwilling to pay cash, a concept they found almost mystifying), it was simplicity it self. They told me it cost $225, I passed over the credit card, done. See you next year.
No need to send paper back and forth between a massive paper-munching machine at the insurance company and a department at the dentist devoted solely to moving paper through that machine. No complicated contracts or regulations. Full pricing transparency -- I know I consumed $225 worth of services, and if that number actually mattered to me I could shop it around fairly effectively.