Hahahaha.
But seriously, no.
The "Superman is a weak character" fallback argument is often used by people who don't actually understand the Superman character, so I'll let you off there.
He's not a weak character, when he's written properly and understood by the writer. I'll admit there has been a lot of bad Superman, in the movies and in the comic books, but that really says a lot more about the state of the people they get to write the stuff than about the character. When Superman is done well - I'm talking about Superman For All Seasons, All-Star Superman, so on and so forth - he's one of the strongest characters in the DC universe.
Yes, his superpowers are fairly all-encompassing, and obviously they get ramped up each and every time the character is threatened to the point where Superman can reverse the flow of time or move a planet if he so wished... but at its heart, he's the Man of Steel, the immovable object and the unstoppable force rolled into one, he's a wrecking machine. If you accept that, accept he needs solar energy to use those powers, and accept his weakness to Kryptonite, at its core it's not a particularly huge deal.
What is actually more interesting about Superman is the character itself, and the stories you can tell. He's both the All-American Hero and the ultimate immigrant, both the living embodiment of the human spirit and an alien, both the saviour of planet Earth and a guy living in a foreign land trying to make a life for himself, both the guy who can defeat any foe and the guy who has trouble getting the girl... you see what I mean. The 'contradictions' as you put them are the essence of the character, those contrasts and dichotomies are what have made Superman so brilliant when he's done properly.
I think we focus, when discussing Superman, too much on the 'Superman' aspect of his character and less on 'Clark Kent,' despite the huge success of Smallville and previously Lois & Clark, which both shifted some of the focus more towards that part of him. Ultimately, Superman is 4 characters, rolled into one. You've got Kal-El, the last son of Krypton; you've got Clark Kent, the Smallville farmboy; you've got Superman, the Man of Steel; and you've got the 'mild-mannered reporter Clark Kent' which is basically his cover story (this is the reason you don't cast a Levi or something). He's trying to be all of these things, and the question of which of these aspects of his personality is the 'true' character is interesting. I happen to think the second one is the 'real' Clark Kent, Superman is just as much of an artifice as the invented, nerdy persona he puts on when he's in Metropolis, but you can have your own opinion on that and that's fine.
Ultimately, there's no actual need to make Superman 'dark' or 'edgy,' because the character actually isn't the two-dimensional, square-jawed jock hero that the people who try to make the 'dark' or 'edgy' interpretations think he is. You don't need to do that to make Superman interesting, you just have to take the essence of the character and write it properly, instead of going too far with the 'he can do ANYTHING' angle or the 'cartoon violence' stuff. What Superman says is that these characters, these extraordinary people with superpowers and fantastic lives, are ultimately people. Clark Kent could've taken over the world the moment he found out about all these powers, but instead he chooses to help people and do the right thing. That says something very profound about the human spirit, when it's at its best, and if that's 'cheesy' or whatever then fine. This is a character who has a troubled history, huge power, a hugely complicated life and destiny, and has to live a lie (or several lies) every day to make a life for himself... he has all of this baggage, and he's still a fundamentally good person at his core, he comes through all of that at makes the right choices. To say that overcoming personal strife and adversity to come out and do the right thing is somehow 'not relevant' to the modern world is beyond stupid.
Give me a good lead (Grifter is right, you find a square-jawed hero and have him play down to be the geeky reporter, so no Levi), a good director, and a writer who understands the character and isn't trying to fuck around with the essentials, and I'll be happy.