Clark Kent works as a secret identity because it's a way for him to fight crime in a different way, while allowing him to be invested in humanity in a different way that allows him to go places and report things and help people that he simply couldn't do as a police officer or EMT (which is especially more important in an era of fake news and yellow journalism, that his invested in truth and justice without using his powers fighting crime the same way). He enjoys writing and jounalism, that is where his passion lies. It is more than just usually powers that defines him and writing allows him to show his skills. Yeah he can easily find a job that better utilizes his powers, but not allow him the same previleges as being a journalist does. Not to mention, even though he is frequently in Metropolis, he is also seen saving people around the world and galaxy as well.
That also is true for heroes like Barry, It makes sense for him being CSI/Police Forensic Scientist (since besides his mom's death, like the above post says he is at his best when he is creative at science and something is extremely gifted at, the speed just allows him to be even better at his job), as well as a full time comic geek/interested in Paranormal activity (I wish we could see more of that element in the comics, tv shows and movies tbh when he isn't fighting crime or solving mysteries). With characters like Clark Kent, Jefferson Peirce and Barry Allen, they are usually written with enjoying or having an interest in their job, or even working in their career before they even get their respective starts at superheroes, and so their identities doesn't have to or need to revolve around them being a superhero, not the other way around.They still find ways to help people, but not in the most obvious or direct ways. Now heroes like Bruce Wayne or Oliver Queen, his identity revolves around Batman, so he utilizes his identity to either help out his crime-fighting career (funding his equiptment, globe-trotting adventures, or setting up to help victims and reformed criminals he interact with as Batman and Green Arrow) as opposed to the other way around. Not to mention heroes with public identities (John Stewart, Zatanna, Guy Gardner). They are known for saving people and they don't need or want secret identities, even though they feel the pains of not having one from time to time, they still find ways of living their lives without letting not have a secret identity than not (John Stewart being an freelance architect, but also lives as a retired Marine sniper or Zatanna performing at shows or doing street magic to get by/she loves the performance aspect of it all).
But then you have heroes who in some way or another grew into the superhero business (Nightwing who grew up in the circus but always have shifting occupations depending on the writer and role, Wally West either goes between public identity or police mechanic if he is written as having a job, Dinah Lance either grew up in the superhero business or police/law enforcement family which influenced her mentality). Marvel shifted into a dynamic, especially around the 2000's with the Ultimate Marvel universe, Civil War and MCU, that it is more natural for the heroes to have public identity. DC seems to have more of a reasonable balance in my opinion when done right.