Homeless people, pee and graffiti are fairly easy problems to solve, and can be turned around quite fast. Lots of places have resolved this.
The sunk cost argument can be overcome if you make public transport faster than cars, less congestion and parking difficulties is a big change. But you do have to rebuild it first (yes the US had public transport in the past, you ripped it out).
They're fairly easy problems to solve, but public opinion of it generally lags behind reality. And the occasional reappearance only strengthens it in people's minds for longer. So even once you've solved it, you still need to wait what are likely to be years to see the general population actually using the system without it being their last resort. During that time, funding threatens to drop because of lack of use. You need people willing to throw massive amounts of money at it until it works, not until it stops making money.
And yeah, if public transit gets better than personal, things will change very quickly. But that path involves trillions of dollars, and just try getting a tax increase voted through for one. I'd love it, but it's not happening any time soon, and certainly not on a large scale.
The sunk cost argument can be overcome if you make public transport faster than cars, less congestion and parking difficulties is a big change. But you do have to rebuild it first (yes the US had public transport in the past, you ripped it out).