There was a (flimsy) historical reason - there had been wars about "augments" in the past; the anti-augments won (somehow), determined the war was about "people setting themselves above their fellow humans", and discouraged more people augmenting themselves/their children in this way by (ineffectively) making it a net negative.
I read somewhere that, in Star Trek land, genetic engineering of intelligent beings is highly correlated with evil, either because it's being done for an evil purpose to begin with or because the engineered beings themselves end up as arrogant, narcissistic jerks with a strong tendency toward becoming evil. The latter implies that there's a technical problem with the genetic engineering of humans that hasn't been solved yet, which Bashir was lucky to have avoided.
Here's the new thread for posting quotes, with the usual rules: