Whether cars should be banned in all town centres is a complicated issue, and one which many people have strong feelings about.
There are some reasons why cars should be banned. Firstly, it would reduce pollution greatly, which is especially important since town centres always consist of tall buildings and narrow spaces which often hold the pollution in one spot. Secondly, with less traffic there would be fewer accidents, and hence society would save money because of reduced medical expenses. Finally, with no cars in town centres there would be no need for large, ugly car parks and parking spaces. This would allow more space for buildings, houses, parks and the movement of buses and people, which could enhance a city greatly.
However, there are some reasons why cars should not be banned. Firstly, it would make it very difficult for many people to travel to work. Most people would have to use public transport (trains and buses) which may become overcrowded and unable to cope with the additional commuters*. Secondly, many people prefer cars because of the freedom it gives them, so banning cars would not be popular, and hence very difficult to implement* since few politicians would support the idea. Finally, cars are sometimes necessary to travel to parts of a city where public transport does not go. Cars are a more flexible transport, especially for the elderly or sick (or lazy).
In my opinion, cars should be restricted from town centres but only during peak hours. It would be impractical and impossible to ban cars completely because they are such an essential part of modern city living, however the problems of pollution and traffic congestion must be reduced. This solution is not perfect but the best we can do, and infact is done already in some major cities like Melborn in Australia.