As people who want to live without cars move to the downtown zone, the area adapts to meet their needs (in terms of the types of stores etc). If the policy proves popular, the city has the option of spreading the "car-less" zone as the dense urban core grows. Similar to suburban sprawl, but inverted, I suppose.
Ironically, those making it unsafe for kids to walk to school, are parents driving their kids being short on time.
Point being, I have not only ever lived in dense urban environments. Secondly, that even those non-dense are perfectly viable to make safe for humans, and use less cars.
Now I live in Melbourne. We use the car very little but would never be without one. I have too many friends in the country and without a car you aren't getting to them without hassle and $. And so the balance of convenience vs cost means we keep the car.