Cities have been designed around Carriages for millenia. You can go and walk in Pompeii and observe pavements for pedestrians, roads for wheeled carriages with crossing spots of elevated stones for pedestrians.
It turns out that cities require a lot of goods to be moved through - more than a pedestrian can carry, and over inclines that human muscle power doesn't like.
The reason why cities are designed around cars is that cars were designed to fit in contemporary cities and they co-evolved over the 20th century. It was the slow kind of evolution, with each step being easier and cheaper than the big redesign.
