This is really about the series as a whole. Why doesn’t Superman just kill Lex Luthor? He knows that Lex will always find some way to create more chaos, so why not prevent it? If it’s because of his moral code, then he could just argue that it is a self-defense from known future attacks.
I'm sure that some comic nerd will come to correct me, but IMHO the Superman of this movie wishes to follow the laws of Humanity, of his own free will, and because that's what his adoptive human parents brought him up to do. So when he defeated Lex Luthor, he turned him over to the human authorities instead of extracting his own form of justice. By doing so, he let the people of the Earth know that he was willing to follow their laws and accept their ethics, and not totally not be a rogue power.
Because if Superman had taken the law into his own hands just after coming to public notice, he would have to be regarded as a rogue power and a potential enemy of humanity. And if he'd ever been considered an enemy of humanity, some military powers might have argued that he needed to be destroyed before he could do real harm, and then what...
I'd still argue he did kill Zod in Superman 2 and I'll say anybody who says otherwise is a mentally ill person who makes up stuff that isn't in the movie because they can't mentally accept Superman killing someone. I don't get why people think he didn't kill him. Why use the ray he used on himself earlier to turn them into humans if he's putting them in the phantom zone? Also there is nothing in Superman 1 or 2 that shows he has a phantom zone projector. There is no way around it! He killed Zod in Superman 2 whether you want to accept it or not!
But in that case, he couldn't turn Zod over to the human authorities, because in that case the human authorities were incapable of imprisoning or punishing Zod. Superman was the only one who could defeat Zod and his minions, and I would presume that by that point the human authorities had some trust in Supes and they knew there was no alternative other than for Supes to defeat Zod by any means necessary.
And Superman did bring Luthor back to jail, just to show that he would go by the book when it was possible to do so.