I think I like your idea better than you do. I'm not convinced of the irrationality of not having a standard utility function such as dictated by the VNM axioms. It's not just a bad description of humans, I think; it's a non-binding norm. I'm not sure exactly which axiom(s) are the troublemakers, but Seidenfeld <pdf> has an interesting discussion.

So I welcome an approach with weaker standards.

Edit: Ha, I picked a fine time to say this.