My experience has been the opposite. Moreover, in a large city, I get to choose my community as opposed to being forced into being in one due to mere proximity.
This is a key, in a city you need to be proactive about it, or if not interested you can fully avoid any interaction and no one cares. In small places, you have to interact at least a little with people around you, or you'll be labeled as a weirdo. And also you're more often in need of someone helping you with something, as not everything is around the corner and readily available like in big cities.
In general, American suburbs infrastructure-wise were built more for cars than people or other transit mechanisms.
Austin seems to care about this a bit less, but I think it might be due to terrain. In general a fence increases home value usually in most Texas cities.
Isolated areas, or at least small towns, tend to have much stronger communities than I've found in cities. Anytime I've lived in a city most "communities" that evolve tend to revolve around work.
Live in a small town for a few years and you'll likely be part of multiple small communities interested in different things. I used to live in a pretty isolated smallish city and knew almost all of the owners of every restaurant I ate at and store I visited. I was active in a range of different communities with many different interests.
If you live in some extremely isolated area, like out in rural Maine, you'll likely be at least acquaintances with literally every person in town. The grocery store clerk and the owner of the town lumber yard will know something about you, at see you as part of their community. When you go grocery shopping it's rare to see only strangers.
Every apartment I've lived in in cities I've only vaguely known my neighbors, but in my first move to the suburbs I was instantly greeted by everyone around me, we exchanged numbers and had a small party.
My experience is that, generally speaking, community increases with the distance from the city center. One particular exception would be a dead zone in certain mass produced suburbs (the ring of death around Denver CO. being a good example).