...Everyone knows that Superman has godlike powers. The cape serves no purpose beyond reminding us of this fact.
...Superman/CK is not a god, and shouldn't act like one. Hence, he should drop the cape, imho.
...Superman doesn't need a cape any more than Clark needs a fedora.
The cape reminds us of Superman being a superhero, whose costumes are always different from what the average person wears.
Superman is not a god, but he is SUPERMAN, and Superman has a cape. He always has.
Comparing the cape to Clark in a hat doesn't fly, no pun intended.
Clark's always been seen with and without the hat. Superman's always been seen with the cape, unless he took it off for some reason.
Superman's costume has a cape, and that's how it should ALWAYS be depicted.
If you can't see that, then I suspect you're not as much a fan of Kal-El as you believe. I'd suspect you're a "passive" fan, where Superman is an occasional tasty flavor you try once in a great while.
Your claim that he can as easily be depicted without a cape is like saying Batman can be. Those two characters have capes. It sets them apart as do all superheroes' costumes...with or without cape. In those two cases, tho', they've always had capes...and I dare say always will.
DC/Warner would be INSANE to depict an onscreen Superman whose costume has no cape. (At least, as a permanent situation.) The fans would never let them get away with it.