The comparisons to Superman with Cena as a character are pretty apt actually.
Fans of comics often blame Superman writers for making Superman a flawless block of invincibility that always won, and it was getting boring. Eventually, the writers for Superman had to find flaws for him. They showed how utterly alien he is, that he doesn't understand humanity in his pursuit for absolute justice has led him to create gulag type super prisons, even a complete dictatorship in alternate universe piece. There've been stories where Superman's very existence was detrimental to the planet he protected. They've explored how even his Justice League members are wary of his both his perfection and his drive for justice. Batman has intricate plans to fight and even kill Superman at any time. Superman was vulnerable now, he was still the Super Boy Scout of Righteousness but at last his flaws (and not pieces of green rock) would lead to his downfalls and overcoming them to his eventual victory. The feeling is that for Superman comics, the stories that expose his weaknesses as a person, as a human, and how it affects his judgement as a Super Hero are the best, and sometimes the only worth reading.
Superman never becomes 'edgy' or an 'anti-hero' he'll always be the Hulk Hogan of comics, it's that they've finally started exploring his flaws that's kept Superman interesting.
The original poster touched on this, but I feel it needs repeating.
Cena as a character will always return to the status quo.
Nothing truly seems to affect him, he'll return to the 'Cena' character within a week or two of any event that happens to him. A hero's tale needs its peaks and valleys. If the character's journey is nearly a flat line, how can it possibly be interesting? Cena 'overcomes' all the obstacles in his way like a hero would, but in the does he really? Do we ever doubt Cena will overcome? There has to be a reason for us to believe Cena can fail, and a reason why we should root for him to overcome. If not, the character
And that latter part is not entirely Cena's fault. WWE's booking of heels in the Cena Era has been pretty pathetic. Name one full time heel, besides the freshly turned CM Punk, you'd believe would beat Cena cleanly (well, cleanly enough, heels gotta be heels). And there's a major part of it, there's no heel that's at the very least Cena's equal. There's nobody capable of challenging the Superman Cena character.
Austin had McMahon, Taker's Ministry, The Rock and the Corporation, DX, The McMahon-Helmsley Era. Hell, Austin's character is irrevocably linked to a match with Bret Hart at WM13 in which he lost. Austin's character is unconscious in a pool of his own blood after losing to Bret Hart, yet this is where discover how tough Austin is, we find our reason to root for him and his character evolved. Bret, acting as Austin's foil, is a major reason why this worked.
This flows back again into the Superman thing. Batman is generally believed to be much more interesting and liked as a character. Batman has the Joker, Bane, Harvey Dent, Catwoman, etc. etc. The Joker's killed one of the Robins, Bane broke the Bat's back, Harvey was one of Bat's closest friends before his injuries drove him to be Two-Face. These are things the character struggled with, showed the reader who Batman was as a character, and how he changed in whatever way because of them. With Superman, you'd probably only remember Lex Luthor's name.
Cena doesn't need to do away with Hustle Loyalty and Respect to be a successful character. He needs to be vulnerable. Not as vulnerable as that lone girl who's been roofied in a bar, but the cracks in the armor have to be there.
Cena has to stop shrugging everything off.
There has to be someone or something at or above his level for him to overcome.
And, he doesn't have to turn heel. He could never turn heel as long as his character has relatable experiences to keep people genuinely rooting for him.
It's probably 90% not Cena's fault he's written and booked this way, so it's hard to dislike him personally. Cena could improve in the ring, he could sell a bit more after matches, he could do away with some doofy mannerisms that make him a little awkward in the ring at times. But so long as WWE is happy with the ratings and PPV buys that Cena has proven he is capable of drawing, we are probably not going to be seeing much change to the Cena persona.
We might disagree that Cena's character is poor or not, but I think we can all agree that it can still be improved, right?