I think its more that the Superman suit itself is an icon. Wolverine and Cyclops and the like aren't defined by their suits nearly as much, they've switched designs numerous times over the years. Superman only really has had one suit and is universally recognized in it, except for awhile when he was a blue energy being in the comic, it was a terrible storyline. He also grew a mullet for a time in the 90s (I'm not kidding).
I think you're right. Notice that in the case of other characters whose costumes are themselves icons (e.g., Spiderman, Batman), the decision has also been to keep the costume.