The solution is not more roadways to magically reduce congestion. It's to build public transit today before it gets more expensive. See the success of the Delhi Metro in India, for example, where New Delhi was never built with a local subway system in mind. [2]
[0] https://www.citylab.com/transportation/2018/09/citylab-unive... [1] https://www.citylab.com/transportation/2018/04/why-new-york-... [2] https://www.globalmasstransit.net/archive.php?id=26471
However, as I said, I believe you (and greenonion) are oversimplifying a complex problem. If you've ever been to any US city, you will see just how much influence the car has had in the development of the entire country. From the principles that you are stating, and that I believe are empirically correct, to the implementation of any viable solution there is a gargantuan gap, and I don't see any solutions being presented. Just "cars are bad, we should use public transport".
And yes, I have been to US cities multiple times, and I don't see why the challenges there are so very different. New Delhi is denser than New York. Its traffic situation was as bad as New York. I am not saying implementation is easy. I am saying implementation is feasible. It's a matter of public and political will. What's holding it back is not that somehow the problem is so complex that it can't be solved.
Adding to the point of induced demand on traffic, thankfully it works the other way too. The traffic situation does not get significantly worse when roads are reduced. The Alaskan viaduct highway in Seattle is an example of this.
Edit: And I have seen the transformation of Vancouver to accommodate bike lanes too, and while Vancouver is nowhere as dense, my point is that the traffic situation did not actually get worse when bike lanes were introduced.
You seem to be forgetting that buildings can't be moved and big infrastructure projects go into the billions. The USA was build with cars in mind, you can't simply undo all that and now ask people to simply get rid of their cars when everything was built specifically for cars.