[YeGoblynQueenne]

>> Does this implicitly suggest that it is impossible to quantitatively assess a system’s ability to understand language? (Using the term “system” in the broadest possible sense)

I don't know and I don't have an opinion. I know that tests that claimed to measure language understanding, historically, haven't. There's some literature on the subject if you're curious (sounds like you are). I'd start here:

Climbing towards NLU: On Meaning, Form, and Understanding in the Age of Data

Emily M. Bender, Alexander Koller

https://aclanthology.org/2020.acl-main.463/

Quoting the passage that I tend to remember:

>> While large neural LMs may well end up being important components of an eventual full-scale solution to human-analogous NLU, they are not nearly-there solutions to this grand challenge. We argue in this paper that genuine progress in our field — climbing the right hill, not just the hill on whose slope we currently sit —depends on maintaining clarity around big picture notions such as meaning and understanding in task design and reporting of experimental results.