I can't say for certain why they are not allowed but I think it has to do with some people going a bit crazy with what they let their dogs do. Some people just let their dogs run wild and of course, this causes chaos and results in dookie being on the beach and in the park.

In other countries I have lived in, dogs are allowed in public places but their are leash laws and penalties for not cleaning up their droppings. This is something I can understand but an outright ban is just stupid IMO.