I'm siding with the people saying a secret identity is going to be almost impossible to keep up, modern surveillance is just too good. I'm also not confident that having Superman's powers would make the rest of the world's opinion of you irrelevant, Lex causes plenty of problems for Superman and he's just one smart guy. If multiple countries are dedicating serious amounts of resources to stopping you, that's thousands of devious people who will be spending all day every day thinking about how to stop you.
I personally, with my normal human range of hearing, already have enough trouble with sounds that I carry earplugs or noise cancelling headphones with me outside of my home. I think if you suddenly added super hearing to that, I'd barely be able to function and it probably wouldn't take someone with comic book genius levels of intelligence to figure that out.