So what makes it okay for Diana to do brutal, lethal things to folks and not Danny? What about Ollie, who's crippled and killed more than a few people during his career? What about Huntress and Manhunter?
Your entire argument fails because with very very few exceptions everyone labeled a super hero is actually a vigilante taking the law into their owns hands in tacit admission that the mechanisms currently in place don't work and some people just need kiling.
The police could be bothered doing anything about it. You know, the social organ we rely on for the apprehension of wrong doers and protection against them.
Batman didn't care enough to do anything -- there's no way he doesn't know about Gotham's forced pornography and sex slavery rings,no way his fantabulous Bat computer isn't cross referencing the faces in all that illegal porn with coroner's reports. You know, they guy who'd meant to be the champion of peope crushed by the jugganaut of Gotham's corruption and evil. How many more people have to get hooked on crack and have what is effectively their multiple rapes filmed and sold to punters before he decides it's important enough to intervene? The only thing he does is take an interest when the folks responsible turn up dead and at that point he if he's any sort of detective at all he has to at least have an inkling fo what's behind it. There's no way that any sort of sane version of Bruce wouldn't have gone into that situation with a strategy to calm and defuse things before he brings her in.
Laws had failed. The system had failed. The people "sanctioned" to operate outside both had failed. The only thing left was one broken young woman with a knife to avenge the stolen life of another and to prevent the creation of any more victims at those men's hands. Not only did she have every right to end them before they could end anyone else, but arguably an obligation to excise those parasitical vermin from society.