The less you invest in public transportation, the more people will drive. The more people that drive, the slower traffic gets. If you just widen the road, all you do is increase the amount of cars that drive. If people can't get to where they are going via public transportation, then they are going to drive instead, increasing congestion. Would recommend watching this video on it:
I think generally what you said is true, but there are other factors. Right now we're in the middle of a pandemic. I'm very thankful I don't have to rely on public transportation.
Yes, if you increase the amount of road and more cars get people to where they are going, the result is increased economic activity. The result also is increased well-being because more people are getting to places where they wish to go - destinations that are improving their lives. This is a success.
You actually see the opposite. Close nit places with more foot traffic and better public transport see higher economic activity and financial resilience. Places with long roads between where people live and where they shop/work/eat _drastically_ harms financial productivity due to higher infrastructure costs. Chuck Mahron makes this point in his TEDx talk. The infrastructure _maintenance_ costs of sprawl dramatically outweighs what a city makes in revenue from taxes they receive.
https://youtu.be/RQY6WGOoYis