Luigi is called a ‘hero’ because he killed a bad person, while Frank Castle and Dexter both kill bad people (literally all they do is kill bad people), yet no one calls them ‘heroes.
And if I write a “superhero” story about a guy with superpowers and he kills every single criminal he meets, from the bank robber to the crime lord, and leaves no criminal alive, he should also be considered a “hero”, more of a “hero” than Superman.
I’ve seen some of the Saw movies and I don’t agree about Jigsaw. Dude basically just captured people and tortured them for fun. Oh, but he was dying. Has been for decades. Just like all of us.
Some people do think the Punisher and Dexter are heroes. Or anti-heroes as others have said. But still heroes. Just not heroes who are virtuous.