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If you want to get technical, the reason Batman has a cape is because Superman had one. Same with the undies on the outside. Bob Kane admitted to just tracing Superman's outline and doing minor changes.




Yes and no. He did use Superman's body as the base image for Batman's form. But originally, he had given Batman wings on his back ala Hawkman. (One of the inspirations for the design being a sketch by Leonardo Da Vinci of a flying machine with bat like wings.)

It was Bill Finger's suggestion that Kane give him a cape, instead. You can still see in the early appearances where Kane gives the cape a more winglike appearance.

Capes are a visual aid in a character's appearance, primarily used in a visual medium. Are they dated? Sure, for most characters. But, Batman's cape still works where many don't. Why does Thor need a cape, for instance? He doesn't. At least, not a bright, red one.