There’s a very real possibility it’s a tragedy of the commons. Each individual wants to be near public transit, but they also want a car to supplement weekend trips and such. But once everyone gets a car, ridership falls and the public transit disappears.
Only if people actually use those cars for trips they could use public transit for. If there's no convenient parking at their destination, they'll leave the car at home.
Here in Tokyo, lots of people have cars that just stay parked at home most of the time, only used for weekend trips. They don't use them for normal stuff because 1) public transit is generally convenient and 2) there's no convenient (or affordable) parking in most parts of the city.
The key to all of this is parking. Parking takes of a LOT of space in a city. Here, there's no requirements about parking: you can build as much or as little as you like. Land is highly valuable, so land owners generally only allocate as much land to parking as makes sense to them economically. So apartments don't have that much (and those spaces cost a lot), and most businesses don't have any. There are some privately-owned parking lots/garages, but they cost a small fortune, and might not be that close to your destination anyway. If you want to buy a building in a dense area, tear it down, and build a parking, lot, you're free to do so, but it would usually be a stupid way to spend your money, so it doesn't happen.
