Tokyo has roads, but household car ownership is 41% prefecture wide; that's well under 1car:1person. In inner city, it is probably close or above 90%. That inner city traffic is pretty much taxis and commercial vehicles. The same is true of any place which is properly built-up with options to get around. Manhattan is another good example: 20% car ownership. In a 2 person household, that's your 90% number!
Building subways is impossible for no good reason nowadays. But it's quite easy to put light rail, bike lanes, and BRT in. People find a way to get around.
You don't need to take cars by force; you just need to let market forces do it. That starts with getting rid of parking, setbacks, and exclusionary zoning requirements for new development in areas of town that are underdeveloped (it's not hard to find these areas in even medium sized American cities). If people really do want cars in those built-up areas, they will rent a monthly space. It's a funny thing though, people seem to re-evaluate how valuable a car is once they have to pay $400/mo for a parking space.
If what you say is true, and everyone truly must have a car, rents will fall in those areas to compensate (developers, not having to deal with onerous parking and setback requirements, still turn a profit). In practice, this does not happen, because places without cars are nice places to live. They appreciate and attract investment, which puts money in the city coffer to improve transit options.
It does not take much land to do this. An area the size of 10,000 single family homes -- often a single neighborhood. In San Diego that's Midway, in SF it's Berkeley and the Sunset, in NYC it's Staten Island. These places all have developers who will break ground in months on collectively hundreds of thousands of new housing units if they are allowed to do it and earn a profit.
It is not fundamentally hard to do this, at all, if you can picture in your mind a human being not owning a car.