[chao-]

I agree that they are ultimately separate and differentiable in a grammatic sense. Mostly I was taking issue with the sentiment in the GP's summary: "Mandarin introduces new grammatical requirements that English ... [doesn't] even have constructs for, like ... counting words." rather than the linguistic specifics.

I firmly feel that, despite being distinct from measure words, they are close enough to English concepts that it isn't really hard to relate to and learn. Gendered inflections are far more inaccessible to me as a native English speaker than counters ever were!