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
The original type of coat that would have been worn when riding was the Great Coat - which did cover the whole body, down to the ankles (and included the front of the body much better than a cloak). Those would have been worn by military officers, particularly.
Those were fine for riding, but then if you were off your horse and end up in the newly developed trench warfare - starting from around the US civil war onwards - you ended up wading through mud which got caked to the coat. So then they started cutting the coats shorter and they became Trench Coats.
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