I guess the difference is that in a game like Skyrim you are kind of creating a character that is in some ways a reflection or an abstract version yourself; perhaps of how you look or what skills you have, or what you fantasise about being like or being able to do. So in that sense, picking a character of the opposite six would sort of feel odd and would suggest that that is how you either see yourself or would want to be! Whereas in games where you don't have a choice you are playing as someone else, as another personality and character, which in some ways is much more of a 'role play' experience than what you'd get in a customisable RPG.
I think you've got a very good point when it comes to what one does as a character and what one's traits are - but not the gender part. I firmly believe that, contrary to popular belief, the playing of female characters and feeling comfortable with it does not imply that the player wishes he were female. In fact, the concept is often so obscure I wonder how the theory came to be in the first place.
See, the first thing you have to think about is that men and women really aren't that different from one another, especially not in a setting like Skyrim. I used to think the differences were massive, but a few years of roleplaying in MMOs has taught me otherwise. Basically, the approach taken by those who know what they're doing there is, "Act like you would on any character and you'll make the most believable female."
I'm not saying there are no differences, of course, but that the differences are slight enough that they don't make any significant difference in what character you play. They only change the way you think you are perceived in the game, and thus change your way of thinking about it. Therefore playing a female character can be a very fruitful experience, even if it isn't really all that special.