For a lot of people for a long time your insurance card (that didn't have a photo) was the only "identification" you had. Otherwise you had to bring your school ID, work ID etc.
Most people don't have drivers licenses cause they take the train. When you sign up for banks etc you usually have to get a bunch of official documentation from the local ward office with your information.
Proof of identity in Japan has always been a bit of a hazy problem. You sign most documents still with a family stamp, so the idea of what legally is defined as identifying is kind of vague.
Most local offices aren't networked up, so when you move you have to register with your local ward office and the japanese beauricratic army goes and gets the previous ward office to fax over your info.
"My Number" is the japanese governments attempt to get all that stuff wired together in one database.
Recent comments by the new Japanese PM stating that an invasion of Taiwan may trigger an "existential crisis" for Japan that would allow them to deploy self defense forces to defend Taiwan.
It's created a gigantic diplomatic and economic fight between Japan and China.