The situation in most US cities is that there are neighborhoods with and without sidewalks. Some subdivisions have them, others don't. And it's not like you can readily add sidewalks after the fact, without wreaking havoc.
In my town, for the most part the neighborhoods without sidewalks also have extremely little car traffic, and pedestrians walk in the street without issue. The drivers also tend to behave themselves.
Changing anything that requires substantially raising the city budget is hard, because the state makes many of the rules for city budgets and taxes. Adding a large seasonal workforce and equipment for clearing sidewalks would be a tough nut to crack. They do clear the sidewalks around parks, schools, and the like. There's also a matter of the preferences of residents. For instance I don't want a ton of salt poured onto the sidewalks in front of my house, and am happy to keep it clear of snow. Every 3 or 4 houses, somebody has a snowblower that rarely gets used.