No. Because increased density goes with less reliance on individual cars. The majority of people (by far) in NY or SF don't have a car already. Traffic is not bad in the densest cities of the western world, because we have much more efficient ways of moving people around: public transit.

But you also need density to sustain public transit. So you have sour spot where there's not enough density to have good public transit, but enough to create bad traffic.

Edit: see below, it's actually the majority of new households that don't have a car in many large American cities, except for NYC, in majority car-free.