Most writers and comic historians that I’ve read seem to feel that it was all Superman’s fault.
Basically, Superman rewrote the rules for comics. Until he came along, the most “superhero” kind of guy you had was the Scarlet Pimpernel… or, perhaps the best example, Zorro. Most adventure comics were, at that time, based around cops, detectives, two-fisted crime reporters, cowboys, and suchlike.
…and then came the guy from Krypton, who could lift cars, beat up anyone, rip down steel doors, and leap an eighth of a mile.
At the time, comics were a highly derivative field. If something sold – or was done by a very talented artist – other companies would imitate the character, and other artists would imitate the artist.
…so super strong guys who fought crime began to appear. In order that you might not mistake them for detectives or cowboys, they wore brightly colored circus suits, and most of them wore capes.
Capes had a variety of practical purposes, too. Considering the horrible quality of the art in many comics, capes were a handy visual device. Perhaps the artist has drawn UltraMan in a running position. UltraMan is running. Yowsah. If we see his cape billowing behind him, we know he’s just jogging, but if that cape is straight out streaming behind him, we know he’s just passed Mach II…
Batman, perhaps, has gotten more mileage out of his cape than any other superhero. First of all, it makes him look bigger when it billows out around him. He can wrap himself in it to make him look creepy and cloaked. He can “cheat” it into big dramatic bat wings. And, best of all, he seems to carry several different capes with him, for different situations. When he’s parked on a rooftop or cornice with the moon behind him, he wears his “Posing Cape,” which is at least twelve feet long and several yards wide, billowing out behind him in the wind…
…but when he’s mixin’ it up with the Joker, he wears his “Fighting Cape,” which can’t be more than three feet wide, and barely reaches the backs of his knees.
(this tradition probably reached its apex with the “Spawn” superhero, whose cape is in fact a living creature, and varies in size at any given time from ankle-length to several city blocks…)
Weirdly enough, in the real world, Renaissance swordsmen studied and developed a variety of fighting tricks with their cloaks and capes, involving tangling an opponent’s arm or weapon, snapping the cape in their faces, or snarling an enemy’s entire head, right before you cold-cock him or stick him through the middle like a cocktail shrimp. In the comics, I don’t think I’ve ever seen a superhero do anything like that.