I'm not sure why your friends are paying that... Most cities in Saitama, Chiba, and the 23 wards at least I know that the 学費 was set as 無償化.

There are some instances where you don't qualify for free school if you make too much money. (Or it could just be they didn't have a good guide at the city office to walk them through the maze of beaurocracy)

Also 23 wards and most of the cities in Saitama and Chiba have daycare and kindergarten entry that's points based(the larger cities have more kids than daycare spots, which is my favorite bit of irony about the Japanese birthrate problems), the more points you have (points based on need, like are you a single mother, both parents working full time etc.)