In my case it's the voice acting. I can't stand Manshep (though I like the guy in other roles) and I prefer ManHawke to FemHawke. The voice of the female inquisitor in SWTOR is amazing while the male one is boring (to me). So for example I'm not willing to endure hours of male inquisitor to play the romances that are only available to males like Ashara.
This is an opportunity games have that movies and book don't. Such a straightforward solution. But people who otherwise are always talking about games as a medium and including player input in interactive storytelling blah blah fall back to the old fashioned, movie/book way of player-independent characterization, convinced that it's impossible for games to go beyond that.
Yeah, when the voice acting works your nerves, that does make it tougher to replay a game for gated content. Typically when I've come up against this, I am already so past the need for "immersion" (I hate this word) in my character that I can just mock the entire playthrough, MST 3000 style, and soldier through to the bitter end. True, it is a less emotionally satisfying experience than my first playthrough, but my curiosity is slaked, and that's enough for me.
Your second point is really interesting to me because it's something I think about often. The argument of how games will be taken seriously as a storytelling medium seems to branch into two opposing arguments, one being "for" games to innovate their own approach to storytelling, capitalizing on the medium's capability of offering choices, the other argument being "against" it- the idea that a majority of the game's elements have to be out of the player's control for the sake of narrative integrity, in imitation of most novels and movies. I am sympathetic to the latter argument (there's a reason that the most culturally resonant stories have not been choose-your-own-adventures), but I do have hopes that the former is something I get to enjoy in my lifetime. 