Certainly, if you make it less practical to arrive by personal car, less people will travel to places by car, and then you'll have less traffic. Unless this comes with a massive improvement in other means of transport, you'll probably have less visitors as well.

The problem with alternatives to personal cars is that personal cars have many desirable properties:

a) near zero latency to take a trip: if there's not a cab at my curb, I have to request it and wait -- or request it early and hope I'm ready when they are. Buses and trains are usually not waiting for me at the station.

b) proportional penalty for leaving late: if you miss a bus or a train by 10 seconds, you have to wait for the next one, which can be an hour. If you leave a couple seconds late in a car, you'll probably arrive a couple seconds late (around rush hour, it gets worse of course). If you don't make it to a requested cab in time, they may leave, and you have to wait for another one to come.

c) availability: a personal car generally provides the same service during the day, at night, and can be used in rain and mild snow (heavy snow, if properly equipped). Busses, trains, and even cabs have less availability at night.

d) flexibility/directness: a personal car can drive to almost everywhere, and can generally take a fairly direct route. Trains only go where there is track, and busses only go where there is a route. Cabs don't always pick up and drop off where you want to go. In case of an urgent change in circumstances, you can change your destination at will in a personal car or cab, but may not be able to easily redirect to where you're going in a bus.