What should your final model be?

In the decision to present the best possible model based on the weight of evidence, should you present the results of Bayesian Model Averaging or of a single selected model based on variables that had strong posterior probabilities in the BMA analysis?

I think you have to present the posterior probabilities. They actually contain MORE information than the selected model. More importantly, the p-values in a selected model don't seem to give a good sense of model uncertainty. This feature is something that I dislike about all automated model selection approaches in that they don't represent competing models that were close to the final model in likelihood but just happened not to be selected.

But it looks like almost no substantive papers use BMA. Why is this?