> I lumped nurseries, kindergartens, and pre-schools under "school". 2-5 year olds will not walk and will not take buses.

For as long as I was in daycare, I was walked there by my parents. When I started school, I first walked, then biked there. It was not until I started grade 7 where any form of transport was necessary, and since then I took public transportation until I graduated.

This was in the suburbs of a mid-sized city (~100k) in Sweden, with comparatively bad public transportation.