So if humans and other animals don't have a utility function, who does?

No one yet. We're working on it.

So the real question is, do humans deviate from the model to such an extent that the model should not be used?

Yes. You will find it much more fruitful to predict most humans as causal systems (including youself), and if you wanted to model human behavior with a utility function, you'd either have a lot of error, or a lot of trouble adding enough epicycles.

As I said though, VNM isn't useful descriptively; if you use it like that, it's tautological, and doesn't really tell you anything. Where it shines is in design of agenty systems; "If we had these preferences, what would that imply about where we would steer the future" (which worlds are ranked high) "if we want to steer the future over there, what decision architecture do we need?".