Oh, i have to drive from single family zone to commercial district to pick up a loaf of bread. Then drive to education district to drop kids at kindergarten, and finally to business district to work.
At the end of the day i hang out at bar/entertainment district with the guys from work to have a beer, but there's no public transport so I have to drink alcohol free so I can drive back home. That's only 120 miles in a day!
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.