True about L&C's specific cape setup, although Superman wrapping people in his cape is a fairly standard image. It's also possible to imagine him using super speed to take off the shirt and cape, and put the shirt back on, but that's kind of meh. He might as well use super speed to rush off and get a new shirt, and that doesn't have a powerful image at all.

Hm, what if he ripped the cape to get it off without taking off the harness? That would choke me up.

Just speculating here... which is the mark of a good story. :-)