The secret identity has worked in various mediums for ummm 75 YEARS!!!!
I somewhat get the "glasses as disguise does not make sense" but we are talking about an alien who looks exactly like a human being who has the powers of a god. Yet doing away with the secret identity will make it more believable???
Superman is a fairy tale, a fantasy. Only with the superficial trapping of science fiction. The best way to explain the secret identity is that is a metaphor. On how we often judge people based on what they look like. Whether race, age, clothing, social status. That also we do not notice or really know people we see everyday at work.