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There are a few things i feel i need to clear up here.

1) I'm not sure what you mean by being unable to handle nonmonotonic/multivariate effects. There is no issue with nonmonotonic effects, the sum of feature contributions is always how each tree actually predicts. Yes, interpretation would be somewhat harder, but can be solved by looking at feature value and/or distribution once you know its contribution.

2) Mean impurity decrease or Breimans feature permutation based method have almost no use in a setting i'm describing. They are both static measures in the sense they only apply to the model itself, and they will tell you nothing about a particular prediction on a data point or a set of predictions on the data set.

3) The issue with highly corelated features is indeed still there, but it is literally exactly the same problem that mean decrease impurity and Breimans method would face.