I believe a fair chunk of the alienation that concerns you isn’t just a result of competitive economic systems, but also urban planning.
When in a city, you have significantly less personal connection to, and knowledge of, the people around you. This makes it harder not only to judge their intentions, but also to punish them. Thus, you are at increased risk when interacting with them (as I think slavojzyzzek mentioned).
Part of the way to combat this may be to turn cities into collections of ten thousand villages. Build each block of the city as a mixed-use unit, with internal green space and, critically, controlled access beyond the shops at the perimeter. That could be as simple as just making people check in when they enter and refusing anyone not approved by a specific resident. Have the block owned or managed by a sort of cooperative responsible for creating cultural festivals and whatnot to encourage social interaction and a sense of community. Specific police officers could be assigned to each block (as the population is high enough) and get to know the residents.
With increased trust and more limited populations, the residents can get to know their neighbors more on the scale of a small town than a big city, reducing the social distance by one or two orders of magnitude. If you’re Communitarian enough, you can also have police/healthcare/etc units focus on specific high-risk people within the block to prevent situations from spiraling out of control.