Your description isn't how it works in most places really. The "districts" aren't usually that far apart. It would be common to find single family homes close by a school, or an apartment building right next to an office building.

Zoning is useful in scenarios like industrial vs residential buildings. You wouldn't want to have an apartment building next to a railroad hub for example. The railroad would be very loud/dirty, and industrial business would benefit more from being closer to the rail hub.