I would totally agree that Shoni should distribute the ball more (much like she did last night) if she had KML, and Stewie, and Stef, and a few other Huskies playing next to her, but she doesn't. She fills her role better than her critics are willing to admit to beat teams like Baylor that few other teams can manage.
We can all use stats to show up a player when we don't want to try to understand her position. You said she never saw a shot she doesn't like, and I just gave you the figure that says that it isn't so. She shoots 48% on two-point attempts, which isn't shabby, and I think Jeff or Geno would say they'd be pretty happy to have a player on their team with that percentage and that taking 13 shots a game doesn't make her a ball hog. Louisville does need to have a 3-point presence to keep teams honest, however, and though they take far less 3s than UConn, it falls to Shoni to plug away with 60% of her shots beyond the arc at a pedestrian 33.6% (though it's still much better than Stewie's, so perhaps you're asking her also not to shoot any 3s? And yes Bria did take 5 3s last night, so Geno still wants her shooting the 3s even if you and supposedly the rest of the UConn fans don't want her to shoot), which obviously brings her overall shooting down quite a bit. Would Slaughter be shooting at 36% from behind the arc if she got the attention that Schimmel gets as the recognized name on the Cardinals? Probably not.
Anyway, it looks to me like Shoni's doing a halfway decent job in her role this year with a Cardinals team that has far fewer resources than the Huskies. I'll check over on LVille board to see if their fans are complaining about her.