Your error is in assuming (or at least not disproving) that natural language cannot fully capture the precision of a programming language. But we already see in real life how higher-level languages, while sometimes making you give up control of underlying mechanisms, allow you to still create the same programs you'd create with other languages, barring any specific technical feature. What is different here though is that natural language actually allows you to reduce and increase precision as needed, anywhere you want, offering both high and low level descriptions of a program.

You aren't stating the obvious. You're making unbacked claims based on your intuition of what transformers are. And even offering up the tired "stochastic parrot" claim. If you can't back up your claims, I don't know what else to tell you. You can't flip it around and ask me to prove the negative.

If labeling claims as "tired" makes it false, not a single fact in the world can be considered as backed by evidence. I'm not flipping anything around either, because again, it's squarely on you to provide proof for your claims and not those who question it. You're essentially making the claim that transformers can reverse a non-reversible function. That's like saying you can reverse a hash although multiple inputs can result in the same hash. That's not even "unbacked claims" territory, it defies logic.

I'm still not convinced LLMs are mere abstractions in the same way programming language implementations are. Even though programmers might give up some control of the implementation details when writing code, language implementors still decides all those details. With LLMs, no one does. That's not an abstraction, that's chaos.