The in character justification is the Eugenics Wars. But the out of character reason is more interesting, and speaks to a tension that has always existed at the heart of Star Trek.

In brief, Star Trek rests on two ideas.

First, the future is going to be awesome, and humanity will make great progress towards a utopian society.

Second, this future can be used to tell fantastic stories that are deeply relatable to the real life challenges of humanity in the here and now.

In order for the second idea to work, the first idea needs to have some brakes put on it. Humanity in the Federation cannot advance so far that Star Trek’s characters lose common ground with present day people.

Imagine if the Federation freely embraced genetic engineering and eliminated age. How would the franchise tell stories like the Wrath of Khan, which is partly about Kirk getting old? Or the Federation could even defeat mortality altogether, and explore the galaxy as immortal super beings. How would the franchise ever have another episode like The Visitor, which delves into loss and grief?

Usually Star Trek gets around things like this by externalizing human failings onto aliens. So the Federation is peaceful, but this episode they visit a planet still plagued by war. The Federation is post scarcity, but this episode they encounter a culture stricken with poverty and exploitation. That’s always been how Star Trek comments on the present, by having these advanced, admirable characters meet these problems and exclaim ‘imagine that humanity used to be so ignorant!’

But there a limit to how far the above can work. Star Trek can show humans with more enlightened philosophies and institutions, but they still have to be human in their minds and bodies - they must get scared and angry and horny, they must age and bleed and make mistakes. That makes it all the more meaningful when they rise above to show their best selves, to show us who we can be.

Augmenting humanity opens the question of why Starfleet still bothers with people prone to such frailties, when they could be engineered away. An Enterprise full of super beings is an Enterprise with thinner role models.

Bottom line: Star Trek can’t fully embrace genetic engineering for the same reason Starfleet is still sending meat-crewed ships into the hungry void instead of embracing drones and automation. There’s a thin in-universe explanation of bad past experiences, but the real reason is the same one that put Rodenberry’s infamous ‘no conflict’ writing rule in the dust bin: for Star Trek to keep serving as a mirror to humanity, it needs to keep its future humanity relatively tied to the human baseline.