"We absolutely understand why it works, if we didn't understand we would not be able to improve these systems" - Understanding how to improve something does not require understanding how it works.

Growing a plant does not imply understanding soil minerals or photosynthesis. Training a dog does not imply understanding it's brain. Using LLMs to improve a codebase does not imply understanding C++. Improving a PC with new parts, does not imply understanding RAM.

You can understand abstractions about the system, without understanding the system. Without gradient descent or other forms of automatic optimisation, do you think humans could build something as capable as GPT-1?

Not sure if this will bake your noodle or not, but yes this is basically my point. Saying I understand how dog training works has very little overlap with saying I understand how the dog brain proteome works, even though they're related, and even though I might (or might not!) understand better how to train my dog for having fully understood the proteome.

Saying we understand training and deploying machine translation systems that have strong predictive (rather than descriptive) power, apparently has very little overlap with defining a formal, analyzable, mathematical model of language. Mathematician who refer to "understanding" generally mean the second thing, but the first thing is also a kind of understanding. Just messier.