As one who has worked in a Japanese hospital for almost 20 years, I have another perspective on health care coverage for foreigners in Japan. My hospital, incidentally, is not unique in providing uncompensated care to those who, by personal (poor) choice, do not enroll in the readily available health insurance programs available to foreigners who are in Japan legally.
Foreign ex-pat health insurance sounds good, but can be problematic for both the patient and the health care provider, since it often has deductibles and excludes pre-existing conditions. Unless there is a contractual agreement between the hospital and the insurer, the patient still has to pay up front in most cases. A large bill of, say, ¥1 million or more can create a major crisis. Most Japanese hospitals cannot direct-bill foreign insurers, comprehend denials, or provide comprehensive medical records and detailed itemized billing in English. In addition, they face long delays in getting paid.
The decision to work overseas is very different from visiting. Immigration is simply ensuring that those who legally reside here have the same access and benefits as Japanese citizens. Perhaps the true motive is to prevent the heavy burden on hospitals from getting worse and to make sure that foreigners legally permitted to be here do not become a burden on society.
If, for example, you are a foreign teacher working on a part-time basis, simply enroll in Japanese national insurance for the self-employed. It is easy, reasonable and avoids financial strain if health care is urgently needed.
I often wonder why foreigners think they should have exceptions to the rules because they don't like them. Health insurance is mandatory if you are here legally and not a tourist. The benefits are identical to those for Japanese citizens. One can carp about the kanji, allegedly poor communications, level of service/treatment, "unique" optional benefits, but you are here by choice. If the circumstances of your living here become unacceptable, you have another choice: Go home.
Opting out of the readily available and reasonable Japanese health insurance plans seems the irresponsible choice. It remains to be seen how the new government will administer the health guideline. Japanese who fail to enroll will also be identified, as they also are failing to pay hospital bills at alarming rates.