An observation: there are, I suppose, a few "flawless" characters out there. Doc Savage comes to mind, and maybe the Lone Ranger or Zorro or Emma Peel, but if you look closely those stories are often more about the people whose lives are effected by the larger-than-life hero (or heroine) than about the hero himself. The Doc Savage adventures are largely told from the POV of Monk or Ham or some more fallible sidekick, who presumably easier to identify with than Doc himself, who comes off as a rather remote, aloof figure.
In my experience, "flawless" characters are usually most effective when viewed from the outside--by awestruck spectators, damsels in distress, dumbfounded bad guys, etc. At least that's how I often like to write them.
That approach doesn't really work with Trek, where (at their best) the characters are more down-to-earth and realistic. Kirk drinks coffee on the bridge, is occasionally subject to anger or self-doubt, needs a vacation once and awhile, and even has a mid-life crisis or two. I like to think Trek is about smart, capable, but very human individuals doing a tough job in space, not pristine examples of human perfection.