I think so too.
However I think there is a misunderstanding between being "deterministic" and "unambiguous". Even C is an ambiguous programming language" but it is "deterministic" in that it behaves in the same ambiguous/undefined way under the same conditions.
The same can be achieved with LLMs too. They are "more" ambiguous of course and if someone doesn't want that, then they have to resort to exactly what you just described. But that was not the point that I was making.
I'm not sure there's any conflict with what you're saying, which I guess is that language can describe instructions which are deterministic while still being ambiguous in certain ways.
My point is just a narrower version of that: where language is completely unambiguous, it is also deterministic where interepreted in some deterministic way. In that sense plain, intelligible english can be a sort of (very verbose) programming language if you just ensure it is unambiguous which is certainly possible.
It may be that this can still be the case if it's partly ambiguous but that doesn't conflict with the narrower case.
I think we're agreed on LLMs in that they introduce non-determinism in the interpretation of even completely unambiguous instructions. So it's all thrown out as the input is only relevant in some probabilistic sense.