This is just another example of Trek's general disapproval of transhumanism, which we also see with their rejection of genetic engineering due to the possibility of Khans (I bet Bashir wouldn't appreciate this being thrown at him during that episode, eh?). The show basically takes any attempt at subverting the natural definitions of what it means to be human as trying to play god and thus something to be abhorred (hence the Borg being the biggest villains around).

The thing is it's not even consistent with itself in how this is applied. How many times do we see our protagonists revived from the brink of death, or even after being dead for a period of time, and yet these medical techniques aren't seen as being an affront to their humanity? What about enhancements like Picard's heart, or Geordi's VISOR? Why are those okay, and Bareil's positronic brain replacements aren't? It gets especially inconsistent when we insist that characters like Data and the Doctor are worthy of being treated as persons, but someone like Bareil is somehow being reduced to something lesser by becoming more like them.

I think ultimately this just comes down to the realities of producing a live-action TV series. If we start accepting cybernetics and genetic engineering then our protagonists cease being humanoid and start expanding outside what a modern audience is comfortable empathizing with. Not to mention that's tough on the budget, and once you've introduced means of prolonging life like this, you have to deal with the consequences for the remainder of the story. Otherwise we end up with a "shooting up tribbles with Khan's blood" situation on our hands.