The same for the public transport -- in cities where rich
people use it, the service is better
I wonder which is the cause and which is the effect here. Maybe some cities were proactive in improving their safety and public infrastructure, and as a consequence have attracted rich people to live there. That's really the only way it will work, anyway - getting anything done in the civic sphere takes a lot of time and effort, and it's not worth it for most people and companies. If cities wish to attract them, they need to proactively improve themselves.
America would be better for everyone if a few more people with influence lived in these places. They'd demand the situation improve.
(The same for the public transport -- in cities where rich people use it, the service is better.)