Oh, one thought here we ought to consider - humankind is NOT the only species to ever work with genetic augmentation. In ST: ENT there was the "Augment Crisis" plotline.
Khan didn't augment himself. The architect of his augmentation was Adam Soong. One of his descendants, Arik Soong (played by Brent Spiner), got hold of some of his ancestor's work - augmented human embryos, which he raised in secret. Arik was the ancestor of Noonian Soong, who crated Next Gen's Data, Lore, et al.
Hilarity ensues. Some of Soong's augment "children" eventually steal a Klingon Bird of Prey. Finding out about human augments, and fearing humans were going to augment their military to beat the crap out of Klingons, the Klingons start their own augmentation research. They find a way to augment adult Klingons (it wasn't great - subjects got stronger and faster, and tended to take on some human physical characteristics and then die due to the DNA mismatchs in neurology).
Worse - one of the Klingon augment test subjects had a virus, "Levodian flu", that interacted with the augmentation treatment. The result was an augmentation epidemic that threatened to kill off all Klingons. Eventually, a cure was found that stabilized the virus, so that it stopped after it had given some human-like characteristics, but before it killed.
This plot was intended to explain why some Klingons (the ones in TOS) did not have forehead ridges, while others (Next Gen and later) do.
But it also explains why the Federation as a whole might eschew genetic augmentation - it nearly destroyed the Humans and the Klingons each in their own turn.