When I was a kid, watching american media, I thought it was incredible that people in TV shows would just leave their houses unlocked and trust their neighbours.
I don't know whether there is any place where people still do this, but in a community where everyone feels they belong and aren't driven to desperation, I could imagine an "open lock" policy working really well.
Everyone locking up their own stuff and blaming people who did not lock theirs down if they get robbed is in itself a form of arms race, which aren't usually optimal.
The idea behind locking doors is to make things slightly challenging for a casual burglar.
My parents live out in a rural area, and they never lock their doors, house or car. The odds of someone driving to their house and burglarizing it are just too low to worry about it - and if someone were specifically targeting their house, they could just break a window and get in that way.
In denser areas, however, that logic doesn't make sense; it's trivial to case dozens of houses in five minutes just by driving down a street.
Locking doors isn't just to prevent burglars, especially if you live around bars. I don't know how many times a group of aggressive drunk football hooligans has got off the elevator on the wrong floor, then tried to get into my apartment thinking it is theirs or a friends. If my door wasn't locked I'd be confronted with 6-7 violent goofs in my living room @ 3am.