Or maybe don't make everyone responsible for the public roadway/sidewalk in front of their house and instead have the people that are responsible for all other things public roadway/sidewalk be responsible?

Works elsewhere, why not in Germany, where taxes should actually be even better able to cover it? [yes I know people in Germany, even specifically in Berlin and no this is not a Berlin specific thing]

Like where I live, the city also says not to use salt whenever you can and use alternatives and they themselves do not salt the roads in our town either, except for the major in and out ones. This is Canada btw. so we do get a load of snow and ice. They use grit and in spring the city sends through a grit cleaning crew (for reuse next winter). Except for the parts that make it onto lawns from snow plows pushing it onto your property. There it's your job i.e. some people put down mats in fall or they use brushes to get it out of the lawn and back onto the street where it can be picked up. Just yesterday, it was above freezing and the city snow plows went and used the warmer weather to scrape lots of ice off the road!