It's never made much sense that the entire multi-species Federation would be subject to a strict ban on genetic engineering due to events on Earth that happened centuries before the Federation was even founded. The way they doubled down on that rationale in Una's trial only highlighted the absurdity -- especially when Admiral April claimed he would exclude Una to prevent genocide.
On the one hand, the writers may be trying to create a straw man out of a weird part of Star Trek lore so they can have a civil rights issue in Starfleet. And that's fine. From an in-universe perspective, though, I think we can discern another reason for the ban on genetic engineering -- the Klingon Augment Virus.
There was a ban on genetic engineering on United Earth, which is understandable given that it was much closer to the time of the Eugenics Wars. Why would that remain unchanged when more time passed, more species joined, and more humans lived in places without living reminders of the war? [NOTE: I have updated the paragraph up to this point to reflect @Value Subtracted's correction in comments.] The answer is presumably that they needed to reassure the Klingons that something like the Augment Virus would never happen again. Hence they instituted a blanket ban around that time -- perhaps in 2155, the year after the Klingon Augment Virus crisis and also, according to Michael Burnham, the year the Geneva Protocols on Biological Weapons were updated.
That bought the Federation over a century of peace, but after war broke out due to a paranoid faction of Klingons who thought humans would dilute Klingon purity and after peace was only secured through the most improbable means, they doubled down on the ban. Una's revelation provided a perfect opportunity to signal to the Klingons that they were serious about the ban -- hence why they would add the charges of sedition, perhaps. Ultimately, an infinitely long speech and the prospect of losing one of their best captains combined to make them find a loophole -- but not to invalidate the ban or call it into question. This Klingon context is why April, who we know is caught up in war planning of various kinds, is so passionate that the ban exists "to prevent genocide" -- he's not thinking of people like Una, he's thinking of the near-genocide they suffered at the hands of the Klingons.
This theory still doesn't paint the Federation in a positive light, since they have effectively invented a false propaganda story to defend a policy that has led to demonstrable harm. But it makes a little more sense, at least to me. What do you think?
Although, it seems to be blanket ban on modification at this point in time. It might have been loosened to allow modification in the case of defects later on, considering that the Illyrians would have no reason to try to devise something to reverse their modifications if modification was allowed, but augmentation was not.
Considering Phlox found that one of their main faults with Earth's genetic engineering program was that they went too far, and tried to create a perfect being, instead of making minor tweaks or improvements, that might be the path that most planets took.
It's also unclear what would be considered "natural" anyway. Even putting aside the Illyrians, we know from "A Measure of a Man" that "mega-strength" is fairly common out in the universe, but just not for humans.
Say a human being was genetically modified to have mega-strength, and telepathic abilities. That's not a naturally occurring feature in most humans, granted, so could be considered unnatural. But a Human/Vulcan hybrid would also have those abilities, and it would be rather silly to consider them unnatural, simply because they were lucky enough to have both Vulcan and Human heritage.