It is my impression that MEP gets rapidly to intersting and potentially insightful results but then further progress becomes much more difficult.
That is true insofar as doing the variational approach with more constraints, the complexity quickly increases.
One of the most interesting domains recently has been in quantifying ecological biodiversity. It works so well that some researchers have suggested giving up detailed modeling of individual species (the explanatory) and simply use the statistical which doesn’t purport to explain succession or niches.This is a state space approach and the species fill up the state space consistent with maximizing entropy.