Actually, I think the insurance policy as a whole hasn't changed much, the visa policy is the one that changed
The insurance problem that we see now is largely caused by the fact that many teachers in Japan were told that they weren't eligible or didn't need government approved health insurance.
This can be largely attributed to the English schools that hire the teachers. Most English schools don't want to pay insurance on behalf of their employees. To avoid footing the bill for the insurance, they made use of loop holes in the insurance policy, so that they were not required to enroll their employees.
To make things worse, many English companies told their teachers that they weren't eligible for kokumin kenko hoken (national health insurance) or shakai hoken (social insurance). As a small benefit, some teachers in Japan were given 'free' health insurance from their companies. A lot of teachers don't settle for this though as the amount of coverage given is sometimes seen as not adequate. As a result many teachers in Japan end up purchasing their own private health insurance.
I have worked for 3 different English companies over the past ~6 years in Japan. I was never once enrolled in a government approved insurance policy! In fact, I wasn't aware of it until recently.
I don't think many foreigners are opposed to paying into this insurance. I think it is the threat of back pay that has prevented many from joining, that and the fact that until now, many teachers didn't know they were supposed to be enrolled.
It looks like
the English industry has a rough road ahead of it.
If you are interested, you can read more about this issue here >
Avoiding Japanese Health Insurance
For information on Health Insurance go here >>
Health Insurance in Japan
Other related discussions >>
Visa renewal and National Health Insurance
Please use the information above as a guide only. The information is believed to be accurate, but not all the details have been confirmed.