It's a matter of practicality more than anything else.

Technically, wearing a cape is still fashionable with black and white tie attire - as well as its military equivalent, mess dress. This is because a cape won't crease the fabrics in the same way that a coat could. Nonetheless, even then you'd be hard pressed to find someone who actually wear one.

More generally speaking, capes have declined alongside the decline of horses. Riding a horse wearing a coat - despite it being warmer, tends to restrict movement in a way wearing a cape does not - which can keep you warm & dry by draping over the horses back. As horses have become largely obsolete, coats - which aren't so easily trodden on when walking on foot, have replaced their role.