How can we assume the models are exhaustive in Bayesian Model Averaging? Bayesian model averaging is justified using the law of total probability which requires the the set of models that we average over to be exhaustive. Shouldn’t  we prove that the set of models are exhaustive first?
Even if you were to claim that this marginal density is an approximation; can w e prove that there exists a set of models which are exhaustive and the set of models that we are averaging in our approximation is a random subset of that?

Clearly, such an assumption will realistically never hold (I'm sure there's some rare situations where it does - e.g. decay of atoms perhaps?). However, it may approximately hold (i.e. there's a couple of plausible models that might approximate the real data generating process pretty closely).
Another justification for model averaging is surely to give the most weight to the model that most closely approximates the data generating process? Burnham and Anderson argue that perspective in their "Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach" book.
