He can certainly afford a cape (he has or acquires a castle every time he pops up in Hyrule, so he's not lacking funds), but he doesn't want to spend his money on such frivolous purchases. Plus, he the rug he wears matches the trim on his boots. It's rather stylish in a classic way.
Also, I do play Falcon under certain circumstances. He's my go-to warm-up character, first of all (until I start trying to do Ganon things with him, signifying that I am warmed up enough). I also use him for the purposes of ridiculous, double kill filled Falcon dittos and if I am playing someone where using Ganon would just be too mean.