>Then again, maybe games shouldn't be purveyors of morality lessons.
I don't see why not. Video games are no different from any other form of information delivery method, except that they're more interactive. Actually, I think this would make them even better tools for helping to teach morality. While you can pick up some morality from books or movies, those are other people's stories in which you're simply an observer. In a game, (especially more modern ones) you typically have more control over the character's actions.
Take, for example, a game which gives you a choice to steal from somebody and, if you do, it shows you the repercussions of your choice. Maybe you come back to that town later and the person is a beggar who pleads with you to give him some coin so he can feed his kids. Or maybe you come back and the entire town is like that because you stole everything that wasn't nailed down. Written well, I don't see why dialog and visual cues like these can't be powerful morality lessons- more powerful than any other teaching method we have except perhaps for real-life experiences.
Of course, the idea is to teach our kids those lessons before they learn them in real life, with real life repercussions.