The original character was supposed to be the best pilot in the fleet and the best card player, so I always saw those two attributes as integral to the role. Also in the original was the conceit that Starbuck and Apollo were inevitably assigned the most important positions in any mission and they carried out a variety of tasks that had little or nothing to do with flying Vipers and I decided to continue that conceit for continuity and for practicality -- you use your regulars to tell story in TV, that's why you're paying them. This is one of those areas where the realism of our fictional universe has to give way to the realism of producing the show. Could we have introduced a new sniper character for the final action scene in "Bastille Day"? Of course. But would that have been as dramatic or interesting as having Kara be the sniper while Lee is in the center of the action? Probably not. Could we have introduced a different pair of shipboard investigators to deal with the assassination plot in "Colonial Day"? Absolutely. But the show is about our group of regular characters, and handing over an entire investigative storyline to two people we've never seen before simply isn't as good as letting Kara and Lee do it -- as long as we can plausibly believe they'd handle those chores. And yes, I think that given the premise of the show, namely that there are only a handful of survivors to begin with and that Galactica herself was undermanned when the attack went down, I can accept Kara being asked to do a variety of roles.
I also frankly enjoy watching Kara take on many of the traditionally male roles in the show, as the leading hero(ine), which more often than not involves being extraordinarily adept at more than one thing. (James Bond, anyone?) Some of it is just my own perverse pleasure at watching us explode gender roles and stereotypes and seeing Kara Thrace be the go-to character in a genre which typically demands that person be a man. And truth to tell, if she were still a he, I strongly suspect that this question wouldn't come up at all.