'Innate desire' is just a fancy way of putting it. I do tend to get carried away with words, being a professional writer (of sorts)
My basic point is that Clark simply wanted to help people, the way a lot of people in the real world help people if they have the means to do so.
But I'm not a fan of the idea of Clark's adoptive parents either being saints who basically raise him to be a superhero, or who crush him with the weight of expectation that he
needs to put the world before himself. Neither am I a fan of the idea of Clark's Kryptonian parents instructing him to become a superhero and telling him its his 'destiny' to serve mankind.
As far as Jor-El 'programming' Superman goes, well again that's just my way of putting it. But it's not too far off. IIRC, Clark really didn't have any idea what he wanted to do with life (apart from maybe wanting to play football and hang out with the cool kids, but being told he couldn't by Jonathan). Then he meets Jor-El, spends 12 years in the Fortress, and at the end of it he has become Superman, with his mission to serve humanity. The implication is very much that it is Jor-El who gave his son the mission to become Superman. This, combined with the whole plot-point in Superman II that Kal-El needs to give up his powers if he wants to be with Lois and no longer serve humanity (as if the two are mutually exclusive) makes it clear that in the Donnerverse at least, being Superman is something Kal-El was indoctrinated to do, and any deviation from that laser-focus of being a hero (such as falling in love) is a dereliction of duty. If you really dive into it, there's something pretty dark there. Or at least joyless.
Absolutely.
I think a lot of people have a certain moral rigidity about Superman and how they perceive him. There may be an ideological/political aspect to it too, who knows?
If you really think about it, Snyder brought Superman down to the basics and took a pretty common-sense approach to the character. He has powers, and he wants to use them to help people in danger. He also wants to know who he is, and where he comes from. Clark is a pretty simple character - the conceit of the film is that it takes this rather simple character and places him in an approximation of the 'real world' with all its complexities and shades of grey. Clark wants to help people, but Jonathan is right when he says that Clark's existence would terrify humanity and turn them against him. Clark finally finds his people, but they turn out to be genocidal tyrants who want to destroy earth and turn it into Krypton. Clark doesn't really want to kill anyone, any more than any normal person wants to, but he's forced into a situation where he has to, and it tears him apart.