I used to walk to school alone when I was little. When I was a little older I walked my younger brother to his school, then I walked to mine. My parents didn't need a car to do that for us.
However all of us used a car to go shopping once a week. A four people family buys an incredible amount of stuff. Sometimes I walked with my mother to small shops to buy fresh food during the week.
We also walked to health care centers. Everything was in a 20, maybe 30 minutes range.
If cities are planned to place homes close to important locations there is little need for cars.