Even cities with world-class mass transit, e.g. Tokyo and London, are full of cars, and taxis are still a better option for some trips -- even though there are also surface trains, subways, and buses to choose from.
In those places, step 1 has already been solved: convince the population that mass transit is desirable and should be well funded. London even charges congestion fees for cars. But they still can't achieve car-free cities.