> But an NN can complete mess up when a new refrigerator is used, that wasn't part of the training set
Not if your training set is representative. And this is just as true of feature engineered approaches, the only difference is that dealing with real world variation requires a lot less work with NNs because once you add the variation to your dataset you're done. With feature engineering that's only the first step because now you have to figure out where the new variation is breaking your features and how to modify them to fix it.
And herein lies a prominent failure mode of a huge amount of this sort of work that I've seen - hard to just "add the variation to your dataset" when your data set is one or more orders of magnitude too small to contain it. At that point all that remains is the handwaving.
The right response to insufficient data is usually simplifying the modeling.
Not if your training set is representative. And this is just as true of feature engineered approaches, the only difference is that dealing with real world variation requires a lot less work with NNs because once you add the variation to your dataset you're done. With feature engineering that's only the first step because now you have to figure out where the new variation is breaking your features and how to modify them to fix it.