I wasn't necessary for him to be Kahn. If they had to do the augments thing, I think it would have been better to make him a member of Khan's crew, and have Khan still in cryo. It never made a lot of sense in Space Seed and STID that the first person they woke up was the leader of the group. From what I recall from Space Seed, they just randomly picked Khan. It could have been anybody.
By waking up someone else, the movie could have essentially been the same, but with the threat of having Khan still available for another (perhaps better?) movie down the road.
Khan's tube wasn't picked in "Space Seed". His tube activated on its own. As McGivers pointed out, the leader was often the first to be awoken so he could assess the situation and then decide whether to revive the others.