I have to assume that by “American Icon” you mean an icon of American culture because:
Superman, tho he protects us in America, is not an American.
He was born Kal-El on the planet Krypton. He came to Earth in a spaceship as his homeland was being destroyed. Upon landing in Kansas, illegally by the way, he was taken in by Jonathan and Martha Kent. Accounts differ as to whether it was a formal adoption or if they just took him in, tho without a birth certificate, how legal could it be?
In addition to being an illegal alien, he’s actually an alien. Not just a refugee drifting toward American soil on a raft, he actually flew thru space in a spaceship.
Even this current depiction of the Man of Steel is not American. He’s a British actor working in the US and Canada on an O2 Visa.
But other than that, spot on