More cars don't require bigger roads. That's exactly the point where pushback has to happen, and does in cities where a compromise works. If increase in traffic does not mean a scramble to accommodate it using your car becomes less attractive, which stabilizes the traffic level. That of course requires a culture which values public transport/bikes/walkability over cars.
E.g. in my hometown every building in the city core is accessible by car, but you have to take narrow, often single-lane side alleys to get there, the major paths all are pedestrian only. All that means taking a car there stays the exception for when it really is useful to do so. Tons of inner-city routes that are faster to walk than to drive. The further out you get, the more car-friendly things get, but public transport bridges most of it. Density is key to maintain that, it makes public transport and local businesses viable and puts pressure on cars.
Making large areas completely pedestrian-only isn't really politically viable, even here in Germany, but the compromises IMHO can work out fine, and people move to areas that have the characteristics they like.
