Care - sure. But what I remember from that scene was two pepole _passionately_ kissing after one of them leveled half a city. What's more, from my observations people who care for each other don't start kissing at a moment like that - they hug.
And Supes clearly wasn't traumatised/shocked at this point.
It's about the message that it sends. Clark Kent becomes Superman because of his upbringing - because Pa and Ma Kent gave him a good example and moral code, he grows into a fine man who decides he's gonna use his powers for good. That's my Superman and I think that's the core appeal of the character.
In this movie we have a weak-ass Papa Kent who keeps telling young Clark to be a nobody.
Also
having his dad die this way means he won't be able to die of a heart attack/cancer later
Except Man of Steel wasn't a documentary, it was fiction. And it's not like he's bad at his job, he's not doing it at all. he doesn't even try to save anyone and saving people is what defines Superman. At least for me, Superman is not about super strength, invulnerability or heat vision, but rather using your powers (whatever they are) to help others. Not because you messed up and a cosmic maniac is going to kill everyone for that or someone made you do it, but because it's the right thing to do.
