There are major axes to accross the city with constant traffic and most bigger blocks are accessible by car (even just for deliveries). But there are pretty large areas with no car entry, and small residential parts are often shared car/bike/pedestrian zones were cars are not privileged.
I also think the goal shouldn’t be car-free, but to have clear separation of the “liveable” space with shops, parks, administrations, schools etc., and the “transportation” space with the trains, cars, cans and trucks. Speaking of Tokyo it often layers the two, with lower level streets/buses/truck roads and upper level walkable space. Seems to be the best compromise, albeit more expensive to build.
I've found Tokyo had surprisingly few cars for a massive city with high population density. Also, virtually no street parking, which makes the cityscape much nicer, and many side-alleys that are largely car-free.
But I agree the majority of locals don’t drive.
Anecdotally last time I was in central London I counted the vehicles going past parliament. About 1 in 10 was an unmarked car, the rest were commercial vehicles or taxis
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.