I just don't understand the double standard. If we think less of the villains because they kill people, why should we think more of the heroes when they do the same? Logically, if killing makes bad guys bad, then shouldn't we admire and celebrate the heroes more if they manage to avoid sinking to the villains' level? If they profess to stand for nobler values but end up reluctantly "making an exception" for the archvillain, or trying and failing to save them, then doesn't that failure diminish their achievement rather than amplifying it?
Sure, yes, you can say it's cathartic to see the villain die. But if we celebrate the death of someone we hate, then why aren't we rooting for the villains, whose whole MO is killing people they hate?
For myself, I root for heroes because they're different from the villains, because they fight for life instead of death. I hate it when fictional heroes are portrayed as casual or frequent killers. Sure, I get that it's make-believe, that nobody's really being hurt so we can indulge the fantasy of violence without guilt. We can ignore the grieving widows and families of all the hapless security guards who were just doing their jobs when the action hero mowed them down, or disregard the thousands of harmless maintenance workers and IT guys that Luke Skywalker blew up with the Death Star, because none of it really happened. But I like it when my fiction stands for something more than that. And when heroes claim to be fighting for life or peace or the rule of law, I want them to succeed in living up to those ideals rather than being forced to "compromise" them out of grim necessity, or being hypocrites with crap like "I don't have to save you." True heroism isn't just triumphing over the enemy, it's triumphing over your own weaknesses and limitations. So if everybody tells the hero he has no choice but to kill his enemy, I want that to be a challenge he manages to rise above by finding a better way that nobody else was smart or brave enough to think of. I'll take Kirk in "Arena" or "Day of the Dove" over Kirk in The Search for Spock. It was Star Trek that taught me that finding a better way is the real definition of heroism.