Out of curiosity, was my caveat "(or at least differentiable) in the region of interest" insufficient for that purpose?
I certainly didn't mean to imply that statistics has unreasonable assumptions. Merely that it tends to have stronger assumptions - and more accurate results - than machine learning. Personally I'm a huge fan of classical statistics and think it's currently underappreciated.
The caveat doesn't work for a technical reason and a more important practical reason. Most relationships, even ones that aren't proper functions, can be transformed into a linear model. An absolute value function is non-differentiable for one value of the input, but it'd be perfectly fine to model with linear regression. More importantly, the audience I worry about isn't the type to pay attention to parenthetical notes using jargon. Linear is somewhat accessible jargon, but differentiable is less so. I'm not claiming that I write clearly, but I aim to write such that I don't need caveats.
Yes it really is underappreciated. As quoted by other comments, "Most businesses think they need advanced ML and really what they need is linear regression and cleaned up data". A significant portion of businesses currently investing millions in ML should basically hire a couple of statisticians and get over it.
To be fair, the fully loaded cost of a couple statisticians (ones who can code, or combined with an engineer assistant) might be half a million or more annually.
I certainly didn't mean to imply that statistics has unreasonable assumptions. Merely that it tends to have stronger assumptions - and more accurate results - than machine learning. Personally I'm a huge fan of classical statistics and think it's currently underappreciated.