This is a bit tangential, but the anime series "Trigun" springs to mind. The character of Vash the Stampede
(very minor spoilers)
Refuses to kill; at all. He lives in a violent world, but somehow clings to the hope that if he just thinks quickly enough he can save everyone with no killing. Sometimes he fails, but he holds himself to the highest standard he can.
(end minor spoilers)
I don't think a comic superhero should kill when it is the best or quickest option. They should do it when it is the only option.
I do think there are definite places in superhero comics for death; some heroes don't refrain from killing and sometimes people die. Just because your heroes don't kill doesn't mean your little campaign world has to be light, or somehow non-edgy.
I think that players in games tend to be willing to resort to killing because they see failing as the ultimate in loss; no one likes to see the bad guy get away in a game. No one likes to get captured. However, to roleplay characters as they existed in the Silver Age one must do so. It has to be okay to be captured or to fail; they must trust that the GM will give them opportunity to make things aright.
As for the player in question, I believe you need to have a long talk about how you want the feel of the game to happen. If this player does not want to play your way you either have to kick him out or let the game change to allow it. Which choice is right is probably not something any of us can help you with, though.