The transit problem is largely a housing problem because mass transit needs a threshold amount of population density to function and that level is below what you get when the majority of the land area is zoned exclusively for single-family homes. But that's not something you can solve overnight -- it takes time to build stuff like that -- so people are still going to have to decide what to do today.
Moreover, even if you build more multi-family housing and mass transit, you're still not changing the nature of the issue, only the scale. There will never be 100% mass transit use because there will always be higher and lower population density areas and some proportion of people living in the latter. Then the people who live outside the reach of mass transit may want to come inside it from time to time, and you'll still have car service for that, and still have peak and off peak, and still have to answer the same questions even if there are only a third as many people doing it.
For sure, but we still have a massive proportion of what could be served by Mass Transit in the States all dedicated to cars, which is why gridlock is basically the American commuting experience in one word. I just spent a week in a major city visiting my employer's office for some face time with everyone, and every morning was started by spending about 20 minutes stuck in traffic, even though my hotel was only a short drive from HQ.
More than three quarters of Americans live in suburban or rural areas. If you tried to run an hourly bus down a suburban street in the middle of the day, it would have one passenger. You can't run bus service at the density of the suburbs, with single passengers it's just a slower, more expensive and less efficient Uber.
Then you get traffic congestion in the city because those people come into the city in their cars. But you can't just add mass transit where the traffic is because those people still need to traverse the part of their path where it isn't.
Moreover, even if you build more multi-family housing and mass transit, you're still not changing the nature of the issue, only the scale. There will never be 100% mass transit use because there will always be higher and lower population density areas and some proportion of people living in the latter. Then the people who live outside the reach of mass transit may want to come inside it from time to time, and you'll still have car service for that, and still have peak and off peak, and still have to answer the same questions even if there are only a third as many people doing it.