All I'm thinking is his identity must be public knowledge because there is no way that he could pull a glasses as a disguise when he's the president of the US. The general public doesn't know who Clark Kent is and he isn't a nationwide figure, so they wouldn't put the two together. Black Clark/Superman as president and no one is supposed to know they're one and the same? Yeah, right.
In Final Crisis, it seemed like a secret identity--but then he had his own version of Brainiac as an AI controlling the White House, so that might be what helps keep the identity secret.