I’m not sure why you brought Superman into it, but I’m very curious since I grew up obsessed with Harry Potter, loved Percy Jackson (though not as much), and I also find Superman one of the most intriguing characters in all media.

In regards to the actual point of your post though, I’m not sure we “identify” with people who have a saving problem. But I think we do all want to think of ourselves as noble and would like to imagine that we would be like Percy and Harry if thrust into those situations.

In fact, I think why those situations are appealing is because in middle school, kids tend to feel out of place, especially nerdy kids who are drawn to reading. Percy got into trouble a lot and didn’t know his father (don’t remember the details perfectly, been a while for me there); Harry was in an abusive household where he was excluded, bullied at school, a complete outcast everywhere. Then suddenly their worlds are flipped in a classic, Joseph Campbell style hero’s journey situation—the most universal story of all time—and they are no longer outcasts but important characters in a vast and powerful world beyond their wildest dreams. And as readers, I think we as kids liked to imagine it could happen to us too, and again, especially kids who felt like outcasts. How many people joked about waiting for their letters from Hogwarts?

I think the essence is those stories call on the deep, mythic and nearly universal (meaning most myths from every corner of the earth share these commonalities) desire to step into something meaningful and important and out of our ordinary lives. I do think their noble nature added to their appeal because not only did we want to join their world, we wanted to be the noble heroes too. But I think those were the cherry on the cake.

A strength in a character also being a flaw is a literary trope from way back.

One of the classic examples is in Sophocles. Oedipus is an aggressive and curious, highly intelligent man. His aggression and restless intelligence serve him well as he is not intimidated by the sphinx, easily guesses irs riddle and claims his prize (the hand of Jocasta). However it is also his aggression that caused him to not submit to the authority of the man who turns out to have been his father, and prompted Oedipus to kill him and his servants, and his relentless curiosity that uncovers the incest he himself is guilty of.

Shakespeare also dealt with the fatal flaw trope, Macbeth is a man of action who excels at making quick decisions. This quality is balanced by his loyalty and humanity. The tragedy is both his and his wife’s : she urges him to act in his own interest, and to hell with loyalty and humanity. As a result he dispenses with these qualities and his best quality turns into his worst as he turns into a ruthless tyrant, who massacres whole families on a whim and doesn’t even care when his wife dies. Her love and ambition for him, her own fatal flaw, turns him into a monster and she dies mourning the absence in her life of qualities she had previously scorned.

I think it was Coleridge who pointed out that if you had put Othello and Hamlet in each others’ play you would not have had a play. Each would have solved the other’s dilemma in five minutes. Othello would have walked straight up to Claudius and stabbed him, and Hamlet would have had one conversation with Iago and walked away saying “that guy is full of shit, and he fucking hates me”

These are all examples of tragedies, but heroic fiction (which is the genre that both HP and PJ belong to) is often basically tragedy with a happy ending. The fatal flaw/character strength which is also a weakness is also a trope in fiction largely because it’s a thing in real life : any strength carried to extremes becomes a weakness, and a strength is only a strength until it isn’t. People often excel at one area of life and so do that thing in preference to other activities, even when it isn’t appropriate. “If your hand is aa hammer, everything looks like a nail”

Superman, by contrast, has no real weakness, apart from the fact that he cares about other people. That’s partly why he is intrinsically a far more boring character than the troubled Batman, and the reason why an external weakness of kryptonite was retconned some time after his creation as a plot device. Stories need conflict and resolution, and a character that incorporates those qualities is just inherently better written and more interesting than one who has it as a clumsy add-on. FYI it was created not in the comics but in the subsequent radio series.