Of course, people being people, many find ways around this! Light "kei" cars, which can actually be pretty big, can be sold w/out the proof-of-parking permit. (Technically, they still can't be parked on-street.) Others may have come to "arrangements" with local authorities.

The parking laws lead to some interesting arrangements; cars squeezed into tiny garages (how do you open the door to get out?); car elevators; multi-storey lots where cars are stacked like battery hens.

In the three #Tokyo neighborhoods I spent time in over a decade, though, the streets were refreshingly free of on-street parked cars—certainly compared to North America, where streets become warehouses for private cars. That makes the streets of many areas a paradise for children...and cats.