I cannot IMAGINE as a foreign resident in Japan getting any kind of social services, driver's license, free schooling, or anything, without solid proof of my resident status here in Japan. There are so many checkpoints along the way, you would never get away with it, for very long, as an illegal in Japan.
You are so right. When my son and now daughter-in-law wanted to marry, my son managed to get a job in Japan, and they went through all kinds of loops and jumps for him to be able to live there legally, and on a smaller scale for us to be able to visit a few days.
Then when they wanted to move back to the states, they spent a small fortune and a good two years, being interviewed by mexicans no less, for her to be able to live here legally.