It's even pointed out in The Incredibles that they are cumbersome.
The Shadow knows! More can be written about this, but you might be interested in these links to start with.
A number of predecessors influences have been suggested.
"Why do classic superheroes wear capes?" : there's dross by current standards, but the top reply by /u/slippyfeet here and the later reply by /u/grantimatter here look useful.
There's more on predecessors in "Where did the idea of superheros wearing capes come from? Why do they all have a damn cape?" : specifically, the top reply by /u/QuickSpore here and the later reply by BaronBifford here .
As for influences after the start, there's Nejfelt's top reply here, in "Why are (many) superheroes drawn or depicted with capes?"
This is not to discourage more discussion. More questions, data, and debate are welcome.