Except Gwen Stacy wasn't a supervillian...
That doesn't matter where the law is concerned. Legally, private citizens do not have the right to employ deadly force, and will get prosecuted for it if they do. And as I explained in the
A-Team thread, self-defense only applies if you had no other choice, no avenue of retreat. If you're a vigilante who actively sought out a confrontation and killed someone during it -- or if you had the opportunity to escape but chose to engage in a fight and killed someone -- then you can't claim self-defense. (Not unless someone else's life was in immediate danger and would've been lost if you retreated, which admittedly is fairly likely to be the case if you're a superhero.)
Laws have to be designed to cover
every situation, not just be narrowly focused on one specific instance. Sure, there may be the occasional situation where the only way to prevent a lethal supervillain from killing a bunch of people is for a superhero to kill them. But that's one situation, not a universal rule. If the law says it's justified for vigilantes to kill, then that sets a precedent that's going to cause a lot of avoidable and unnecessary death, including the death of innocents, because not all vigilantes are going to be as responsible, careful, ethical, or unprejudiced as a Superman, and because sometimes innocent people get accused of crimes. So the law has to come down hard on lethal force for everyone's protection. Exceptions exist, but they must be narrow. And it's not up to the police to say "Aww, we'll look the other way this time." They don't get to decide which situations warrant exceptions to the law and which don't. That's for the judicial system to decide, and the superhero would still need to be investigated and questioned in order for the DA to decide whether criminal charges were warranted, and possibly arrested and put on trial for a jury to decide guilt or innocence. And even if the superhero were cleared, their secret identity might still be exposed and their effectiveness as a superhero undermined. So again, it's in a superhero's best interest to avoid lethal force if at all possible, from a pragmatic perspective as well as a moral one.