Historically, and in some countries still, we solved this problem by identifying when it was happening and creating new public transport lines for faster commutes and people living further out. In the UK, we even developed whole "New Towns", upgraded their transport, amenities and infrastructure specifically to support shuttling a greater number of people into London. They weren't particularly inspiring towns, and we still make fun of them nearly a century later - but it worked. Even today, it's far quicker to take the train into London from those towns than it is to drive, as is the case for pretty much all suburb to central commuting here.
There are still lots of situations where a car will be better (I have one too, in London), but if we can get people out of their cars for their commutes, that frees cities up to expand and useful houses will become more affordable. Driving to the tip or mall is much less of a problem.
Regarding the violence and antisocial behaviour, that's really a problem of policing and allocation of funding. It needn't be that way and it doesn't happen to nearly the same extent in the UK and I put that down at least partially to the excellent British Transport Police. Apparently it used to be violent and dangerous in the 80s but we turned it around. Now the train stations are mostly far safer than the surrounding environs. If I was ever being harassed or attacked, I would run towards the station as there would most likely be someone to help me there. Living within a few minutes of a train station also significantly increases your property value here, provided you're not so close that it rattles your bed...