"People should aim for their behavior to satisfy the VNM axioms."

OK. But this seems funny to me as a moral prescription. In fact a standard premise of economics is that people's behavior does satisfy the VNM axioms, or at least that deviations from them are random and cancel each other out at large scales. That's sort of the point of the VNM theorem: you can model people's behavior as though they were maximizing something, even if that's not the way an individual understands his own behavior.

Even if you don't buy that premise, it's hard for me to see why famous utilitarians like Bentham or Singer would be pleased if people hewed more closely to the VNM axioms. Couldn't they do so, and still make the world worse by valuing bad things?

If your goal is "to do the greatest good for the greatest number," or a similar utilitarian goal, I am not sure how the VNM theorem helps you.

Yes, that's why I think of "people should aim to be VNM-rational" as a weak claim and didn't understand why people appeared to be against it.

Is "people should aim for their behavior to satisfy the VNM axioms" all that you meant originally by utilitarianism? From what you've written elsewhere in this thread it sounds like you might mean something more, but I could be misunderstanding.