The second it becomes a possibility, a significant percentage of people will flee the things that they have difficulty tolerating, simply because they no longer need to tolerate it.
This is people everywhere, dense or sparse—the difference is that in a denser city you have the ability to choose to engage with people who satisfy your standards, unlike a small town or suburbia where it is more about whom you happened to have living nearby (count them on your fingers) and whom you have to acknowledge whether you like them and agree with their mores or not.
I find this much more of an issue psychologically in smaller towns and countryside, where each individual ends up knowing much more about each other because there’s just no way around it (and whom sparseness and subsequent lack of things to do pushes to alcoholism, drugs and other vices). In a denser area I physically couldn’t care what each of the hundreds of strangers I come across every day does in their spare time, people tend to follow a certain protocol in public interactions, law enforcement is more efficient due to constrained area, and it generally feels safer and more respectful of my attention and privacy as a result.
Problems like degraded mental health (and resulting substance abuse, high crime rate, etc.) can probably be exacerbated and contagious in denser areas but I think they are more prevalent in sparser ones.