In fact, I believe autonomous cars will increases a city's ability to network, because it increases people's ability to aggregate into a single place. It will also make the city an even more desirable place to live and work, because autonomous vehicles reduce the pain of moving around in the city.
Population density is correlated with increased rates of mental illness.
(mind, I'm asking this with the assumption that mental illness is much broader than just homeless schizophrenics, so to speak. I can definitely see why they might gravitate towards heavily populate areas. But they usually don't pay rent.)
But other drivers might be that certain demographics are more prone to living in cities as well as developing mental problems: immigrants who are under a lot of stress because of having to adapt to a new language and environment; people in high-pressure jobs like lawyers and people in finance; criminals; etc. (being a criminal is very stressful and most non-psychopath criminals who have been living such a lifestyle for several years or more develop stress-related physical (ulcers, ...) and mental problems because of it, potentially on top of the mental problems they had before).
Or maybe people with mental problems find it easier to be anonymous in a city, where they don't have to (or at least less) deal with the social pressures that outsiders in small communities are under.
Furthermore, while statistically there are more people with mental problems in cities, some classes of problems (like depression) happen more in more rural areas.
I'm not saying one or the other; we don't know. Every now and then there is a study in the popular press with a populist headline like 'cities cause mental problems', and it's also an idea that fits nicely with people's preconceptions about cities=bad, country life=good. The papers those articles are based on are not conclusive though, and the literature shows a much more nuanced image. I work in academia and peripherally work with social scientists who study cities and people living in studies, and they are much more uncertain about the health implications of cities. There are sometimes unexpected feedbacks in complex systems that can cause very unintuitive dynamics.
Higher residential density would be survivable IF "work at home every other day" was somehow legally enforced. That would maintain the face2face fiction while also increasing density without collapse due to congestion.
Automated bulldozers and high-rise house-building machines, though ...