I don't think people recognizing that Clark Kent looks like Superman is as big a danger as people make it out to be. There are plenty of people who look like famous people. There are enough of them that there are look-alike contests for it. Superman's a few notches above being a celebrity, he's kind of more like a god. I doubt most people in-universe even think Superman has a secret identity. It probably hasn't even crossed their minds that he does anything other than be Superman. They just write Clark Kent off as some guy who happens to kind of look like Superman.