Not trying to argue against most of your points, but if you re-read book 1, you realize that people hate Sansa because (at the beginning of the story) she's a little brat who brazenly ignores what her father tells her to do and, in so doing, gets him killed and her entire families' lives (her own included) utterly destroyed (remember that while Ned idiotically warns Cersei that he's going to rat her out, it's Sansa who shows up and provides Cersei with all of the details of Ned's plans, in the process of whining about having to leave the city).

Obviously she grows a great deal as a character over the course of the series, but it's very easy to start hating her early on, and that kind of impression can be hard to let go of.