If M1 were so general that by judicious choice of θ you could impose an arbitrary distribution on X then you’d pick the distribution that has P(X=x⋆)=1, where x⋆=argmax(u). That is, a distribution where HM1(X)=0.
For me, that detracts a little from the entropy + KL divergence decomposition as applied to your utility maximisation problem. No balance point is reached; it’s all about the entropy term. Contrast with the bias/variance trade-off (which has applicability to the reference class problem), where balance between the two parts of the decomposition is very important.
It’s not quite all about the entropy term; it’s the KL-div term that determines which value x∗ is chosen. But you are correct insofar as this is not intended to be analogous to bias/variance tradeoff, and it’s not really about “finding a balance point” between the two terms.