To state, as you have done, that you believe Japan's health care to be better than other options, is indicative of not having any idea of comparables. Is it cheaper? In terms of what one pays for an individual hospital visit, yes. Is it cheaper when merging cost and performance? Not even close. It is, by that comparison and absolute disaster.
I am really not sure either way. I think it's clear that Japan has cheaper health care than the US, and that the US has some of the best health care in the world if you are able to pay a lot for it, but I wonder whether there is really more value added in the US system.
A key aspect, overlooked in the above discussion, is the relative lack of tort claims in Japan. You can sue your doctor for malpractice here, but you are more likely to get a few thousand dollars than a few million dollars, and you also can't hire a lawyer on contingency in Japan, so you need to post a lot of your own money up front in order to sue. The lower risk of lawsuits feeds into a lower overall cost of health care. I'm not saying which way is better -- that has actually been a pretty big legal debate in Japan. The American way raises costs for everyone, but also helps to push riskier doctors and crappier methods out of the system. In Japan, on the other hand, you are pretty much SOL if your doctor does something stupid, and as a result there are quite a few doctors who do stupid things throughout their careers...