I have only skimmed this and am planning a careful read, but my first impression is that Wald’s complete class theorem is exactly the desired coherence theorem. Complete preferences seem like the weakest possible assumption one could make and still expect to show non-Bayesian decision rules are dominated. If you want to show that “want something → should use Bayesian decision theory to get it” there is no need to argue about the premise that an agent wants something, and to me wanting something coherently requires complete preferences.
I have only skimmed this and am planning a careful read, but my first impression is that Wald’s complete class theorem is exactly the desired coherence theorem. Complete preferences seem like the weakest possible assumption one could make and still expect to show non-Bayesian decision rules are dominated. If you want to show that “want something → should use Bayesian decision theory to get it” there is no need to argue about the premise that an agent wants something, and to me wanting something coherently requires complete preferences.