We finance the baseline of education/transportation infrastructure from public funds because we believe that improves productivity, and performance of civic duties in a democracy across the board. Purely privately owned education/transportation is politically contentious for various reasons, right? Enclosure of the commons, economic inequality, limited avenues for upward mobility and all that, right?
Lastly, a pedestrian on city-founded sidewalks is "a private citizen occupying public space" just as well. There's no moral qualitative difference between an individual pedestrian, an individual on a bicycle, an individual in a car [1], or a group of individuals in a tram or bus. We can argue about occupancy and all that, but that's just quantitative difference of maybe an order of magnitude at worst. The use of public space should should primarily support the main activities of the general public.
[1] pollution from ICEs aside, but we're on track to fix that permanently.