Not to mention the idea that JR is only 7% of Japanese railroad makes little sense in real life. JR carries a majority of rail passengers in Japan. The long tail of non JR railroad companies in Japan are small, regional operators owning maybe one or two lines with infrequent services. Many of them are also private only in the sense that they are incorporated in the same way as private companies. But if you dig a little around you will find out they are actually owned by local governments.