> have a total of 3-4 locations to visit daily
I'd argue that the problem is not roads themselves, the problem is that cities are built around roads and cars. If cities would be organized with being road-free in mind, the problem you're describing wouldn't exist.
A lot of cities in Europe have changed their way of thinking how to design a city these days, and try to evolve the downtown areas so that they're closer together and easier to reach via public transportation and/or by foot. Just some examples that come to mind: Venice, Granada, Amsterdam, Heidelberg, Nuremberg, Rostock (and soon probably Mainz and Stuttgart, as they're actively working on it).
What these cities have in common: They changed their prioritization from multi-lane roads inside the city to a sustainable park&ride model that embraces cheap and regularly available public transportation, and combines that in worst case (when they don't have trams, busses or subways) with something like rentable bikes provided by the city. In best case, you'll have something like Amsterdam or Venice, where everything is not built for cars but for all other modes of transportation, except cars.
And some might argue that those cities have working plumbers, hairdressers, dentists etc, too. They seemingly can still work without having a multi-lane highway blocking the skylight over their houses. Why do you think is that the case?
Plenty of other roles that can't be performed remotely, e.g. plumbers, hairdressers/beauticians, dentists, shoe/clothing store workers, therapists, teachers (technically possible, just not desirable in the last two cases).
But that's not even the limiting factor for public transport: the landscape of extracurricular activities for children shifted.
Parents of children too young to cross the whole city on their own have a total of 3-4 locations to visit daily. Doing that via public transport quickly becomes tedious.