Because Spock has already told the audience this. He doesn't need to repeat himself.
A. Spock doesn't know the audience exists.
B. Even if you establish certain details earlier, it can be repeated if those details actually does something. If fragmented records are such an essential part of understanding the dark period of Earth's history, there is no reason why it shouldn't have factored into Spock's arguments when the crew spoke admirably about him.
Plus, aren't you missing the whole point of the episode itself if you're just going to paint Khan as a bona fide bad guy who wants to kill everyone? Space Seed was about an ambitious and ruthless dictator who wanted to start a new life and build a new world away from the inferior humans who over threw him. The one element that is more important than his history on Earth is his superior ambition. We saw that when planning to take over the Enterprise how he was going to attempt to take on the galaxy instead of just the world. When Kirk finally defeated Khan, he gave him what he wanted in the first place. A fresh, unpopulated world that he could build however he saw fit.
Spock: It would be interesting, captain, to return to that world in a hundred years and to learn what crop has sprung from the seed you planted today.
Kirk: Yes, Mr. Spock. It would indeed.
That's a much better way to represent Khan's character than... well, this.
Spock: Khan Noonien Singh is the most dangerous adversary the Enterprise ever faced. He is brilliant, ruthless and he will not hesitate to kill every single one of you.