That's commercial traffic, car-free policies are usually designed with support for commercial vehicles. It's really about eliminating private automobile traffic in city centers. If you mean going to the store to buy large items, delivery is probably the solution there. Deliveries like that can be grouped into a smaller number of larger vehicles, or done at off hours, or only on certain roads, or all sorts of different things.
Car-free isn't the greatest moniker in the world. It really means eliminating private automobile traffic, not eliminating vehicles altogether.
> Also public transport often takes much longer than a car, because it's stopping at every little stop, while a car can go directly, or even take a shortcut in some cases.
This isn't typically true in dense urban areas with high quality transit networks. Those are the areas that are suitable for car-free. Certainly most places would suffer greatly from the elimination of cars, but those areas aren't the target.