I'll add another country with even better public transport (especially trains) - Switzerland. A small, dense and very wealthy country that has train station at the heart of every city and many villages, and the rest is covered by buses.

Yet every single morning and evening there is huge traffic jam around every city. Every single year highways are more full, more issue with parking.

If it can't be solved in such ideal country for public transport, I am not holding breath for rest of the world, and just wishing something ain't gonna make it real. There are many reasons why situation is as it is (it costs a lot, even such transport doesn't cover many people's cases well enough and nobody wants to spend 120 mins every day commuting via public transport when its say 60 with cars).

What I can imagine actually working - uber style shared robo (meaning cheap) taxis/minibuses. Big enough network that one can even switch a car in some 'taxi station' for more efficient trip that would take just marginally longer than driving oneself. This solves a lot of parking issues in cities and would reduce traffic to maybe half or a bit less.