for starters, ZOD HIMSELF exposed the hypocrisy of the Kryptonian government, which was why he organized a coup in the first place. when him and his people were being sentenced for treason and murder, he exposed their hypocrisy and told them that Jor-el was right and Zod was only doing whut HE felt was needed to save the planet from itself. This is actually an allegory of our government, or should i say the governments worldwide taking things serious for granted that are destroying our world. this shows that even though the eyes of armageddon a government will take things for granted.
also, you are absolutely correct, and both goyer and snyder stated that many will sympathize with zod due who his purpose. zod was born, bred, and trained for ONE SINGULAR PURPOSE and that was to PRESERVE THE LIFE OF KRYPTON by any mean necessary. he even confessed that he HATED the fact of killing Jor-el but knew he'll do it again, because his directive is the only priority. so, technically, whut HE was doing was actually NOBLE. the only difference is he refuse to be identify himself with humanity, which by definition makes him inhumane, nor do he believes in individualism which was the COMPLETE BEEF between him and Jor-el who wanted his son to make his own decisions and life and be who HE wanted to be free from any oppression. both of them had IDEOLOGICAL differences to which put themselves divided among each other.
you can ALSO view superman as a SELLOUT which you won't not be wrong in doing that. bare this in mind, superman since his INFANCY been bred as a HUMAN. humanity is ALL HE KNOWS. he knows NOTHING about krypton, about that world, about that government, virtually nothing at all, and do not understand at all ZOD's view of things of him preserving the lifeline of krypton. he doesn't even know that he carried the DNA of all the kryptonians that ever existed. in his mind, he just sees ZOD as a threat to mankind and he has to stop it. he never saw himself as a KRYPTONIAN and has NO ATTACHMENT to that world, hence why his choice of saving humanity over kryptonians was so simple to make.
ZOD didn't care if he had super powers or not. as i stated before ZOD's life long dedicated DUTY is the PRESERVE the life of KRYPTON and nothing ELSE. ZOD saw the beacon coming from the ship on earth, went to it, found the reserved life cells from that ship, learned that superman carried the codex DNA of all kryptonians, so NATURALLY it's time to set up shop. his MISSION was all about PRESERVING krypton, so he had to terra-form the earth to make it like krypton for life for KRYPTONIANS to live in. at the same time, it forces superman to lose his powers which makes it easy for them TO KILL HIM and suck the codex out of him. knock two birds with one stone.