This is basically right, but I guess I think of it in slightly different terms. The KL divergence embodies a particular, implicit utility function, which just happens to be wrong lots of the time. So it can make sense to speak of "better_KL", it's just not something that's necessarily very useful.

Note also that alternative divergence measures, embodying different implicit utility functions, could give different answers. For example, Jensen-Shannon divergence would agree with instrumental rationality here, no? (Though you could obviously construct examples where it too would diverge from our actual utility functions.)