As for the comparison with ML, I think a large chunk of the ML community aims for (with good reason) evidence of predictive capacity rather than theoretical soundness. Not everyone. I'll grant that a good portion care deeply about theory. Look at the arguments between SVM folks and "Neural" Nets folks.
It comes down to a difference in focus. Statistics cares about causal inference. Machine Learning cares about prediction. Nothing wrong with either, but theiir techniques are sometimes ill-suited for the other purpose.