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?
This is the real answer. For many more questions too. One day in the distant future people will ask why don't we ---- anymore and the answer will be because we don't drive cars anymore.
You need to stay warm, but you can't have your legs blocked by something like a trench coat (unbuttoned cowboy duster excluded), since you need them free to mount and sit on a horse. A cape keeps you warm, but keeps your front lower body free to ride, and lays flat against the horses back when mounted. Since we ride in cars instead of on horses now, the design isn't very useful anymore. A long cape will get in the way when getting into a car, and when sitting down in a car seat. Jackets and coats are more practical now.