The Japanese problem
As opposed to our New Urbanist friends, Japanese largely dislike on-street parking. It's important to point out how narrow most residential streets actually are, being around 5-6 meters only (16-20 feet), without sidewalks. So if there was a lot of cars parked on the street, it would quickly become unlivable. It's fine if there is a car parked temporarily on the curb once every block or so, but the usual unbroken lines of parked cars we see in many North American and European cities would be disastrous. Streets would have to become one-way and pedestrians and cyclists would find it hard to coexist with moving cars on the street.
What to do? What to do?...
The Japanese solution... proof of parking
Basically, Japanese authorities decided that finding off-street parking places wasn't the government's responsibility, but the individual car owner's. The government just makes sure that the car owner does find one. They did this by requiring a proof of parking for people who want to register cars.
Let me rephrase that: in Japan, in order to get license plates for a car (which is necessary to use them on public streets and roads), you must prove that you have a place to park that car off the street.
What happens if people don't have this proof? Well, they essentially cannot use their car except off-road, so there's no point to buying one.
However, it's important to note that the point of this rule ISN'T to keep car ownership rates down by preventing people from buying them. If this was the objective, it failed miserably... there are about as many cars per capita in Japan as in Canada.
People who want a car but don't have a place to park it on their land (if they own it) then need to find a place that will allow them to rent parking spots. If they find one, they simply have to pay the owner of that parking lot to rent a spot, the owner will then provide a proof of parking and they've solved the problem. Since there is money to be made by offering these parking places, some enterprising people will usually provide them, but at a cost depending on the cost of land and of building the parking lot. In rural areas, parking is very cheap, in big cities, it is very expensive and may dissuade people from owning cars.
This isn't punishing urban car drivers, it's just about having them pay directly for the cost of the parking for their car. In North America, we still pay for parking, it's just bundled in other prices so that we don't notice it, so parking is heavily subsidized.
This system works very well. It avoids creating an oversupply of parking or forbidding density. There is only as much parking available as car owners are willing to pay for. If there is a great demand for parking spots and that people are willing to pay a great deal for them, then parking lots or garages spring up. If there is too much parking and parking lot or garage owners can't justify owning that land for parking anymore, they sell to people who want to build houses or apartments instead.