After spending over a decade in both statistics and machine learning I'd say the only reason there isn't a "broad consensus" is because statisticians like to gate-keep, whether that's linear regression, Monte Carlo methods, or Kalman Filters.
Linear regression appears in pretty much every ML textbook. Can you confidently say, "this model that appears in every ML textbook is the only model in the ML textbook that isn't an ML model"?
Kalman Filters are like a continuous-state HMM. So why are HMMs considered ML and Kalman Filters not considered ML?
IMO it's an ego thing. They spent decades rigorously analyzing everything about linear models and here come these CS cowboys producing amazing results without any of the careful rigor that statisticians normally apply. It's difficult to argue against real results so the inflexible, hard-nosed statisticians just hang on to whatever they can.