Attitudes vary about fences in different areas. There may be a thesis study here, comparing the 'fence behavior' of people in different parts of the country, and with different income levels.

Nearly all back yards are fenced here (Calgary, Canada), whether the owner has animals or not. In a new neighborhood, working out the style and shared cost of the fence with neighbors is one of the first jobs of ownership. If agreement can't be reached, the dissenter usually builds the fence on his property rather than on the property line. Sometimes the property line becomes the no-communication line.
Front yards may have a low hedge or low fence, but the city bars tall fences except for the back yard.

A long time ago I had a house in Tulsa, OK. The land was developed as a no fence area. Backs of houses were separated from those behind by broad expanses of grass, very attractive and uncluttered. It worked pretty well, but wandering kids and pets sometimes caused minor problems.