I understand that modern outer layers are more functional. A leather jacket, for example, can be dressed up or down so as to be worn in a variety of situations. It is also better at keeping you warm.
However, I think capes/cloaks are more aesthetically pleasing garments. It also feels good to have the fabric flowing around you as you walk. But what do you think?
The other big reason is that the world is cleaner. Capes and cloaks also protect the whole body from mud/dust and can be easily removed. Riding a horse or walking on dirt roads is a lot dirtier than riding in cars or walking on a sidewalk