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.
But having to pay for it directly sounds extremely counter-productive.
And even the first part is dubious really: there should be sidewalks most everywhere including non-residential locations or the like, which the city would almost certainly have to clear alongside the roadway. Surely in that case itβs more efficient and simpler to just clear everything uniformly?