You have to factor Cultivation into this equation, though. If Odium and Honor balance each other out, what does Cultivation's presence do?
Honestly, I saw very little honor with Shallan. Don't get me wrong, she's a good girl and all, but honor isn't a motivation for her, as it is for Dalinar and Kaladin. She's attracted to her studies; science, art. Culture, you might say. Jasnah is the same way.
If Odium is "the most terrible of all the sixteen," then it would make sense that Honor and Cultivation would throw their lots in together against him. I think the different kinds of Surgebinding come from different combinations of the two.
But aside from that, I do agree with the Intent thing. If the magic systems didn't have anything to do with Intents, then there would be no reason to have Intents in there at all.