The last scene they needed him to truly care about and actively try to mitigate fucking civilian damage and death. Make that a real weakness that Zod takes advantage of during the fight. I saw a clip of a modern superman cartoon and it seems they do the same back and forth and superman doesn't seem to factor in civilian damage and death. What the hell is a point of a hero then? Where is the god damn emotionality and vulnerability? In a city full of people, they are a factor to the old superman and should be for the new as well.
That last killing of Zod too was horrible and just not in line with our classic and heroic superman. Hero's especially all powerful ones must set limitations for themselves based on morality for us to really feel it. It's not just about picking sides of humans or kryptons Superman needs to be morally above everyone else.
People will never be able to relate to the godlike superman, they can only emulate his morality, willing to sacrifice, and extreme will to try and save people even if it is strategically bad in a battle and he is physically hurt as a result. Kids can dream about about flying and super strength but Superman's unwavering lawful good persona, unwilling to sacrifice people, and save everyone he possibly can is what kids look up to emotionally.
Even if Nolan made a dark and gritty Batman he did a good job with the persona of the Batman, capturing desperation, sacrifice, and heroicness. Wish he could have imparted some of that to this team with his involvement here.