I don't think I'm being pedantic or narrow. Cosmic rays, power spikes, and falling cows can change the course of deterministic software. I'm saying that your "compiler" either has intentionally designed randomness (or "creativity") in it, or it doesn't. Not sure why we're acting like these are more or less deterministic. They are either deterministic or not inside normal operation of a computer.
To be clear: I'm not engaging with your main point about whether LLMs are usable in software engineering or not.
I'm specifically addressing your use of the concept of determinism.
An LLM is a set of matrix multiplies and function applications. The only potentially non-deterministic step is selecting the next token from the final output and that can be done deterministically.
By your strict use of the definition they absolutely can be deterministic.
But that is not actually interesting for the point at hand. The real point has to do with reproducibility, understand ability and tolerances.
3blue1brown has a really nice set of videos on showing how the LLM machinery fits together.