The thing is it doesn't really prove LLMs can't do this, it proves no existing frontier LLMs can do this.

The part where they talk about sampling multiple runs is interesting - it suggests to me that in the next few years as the reasoning process is improved the models may be able to do that autonomously.

My mind really is going to using a dedicated object detection models fine-tuned with nutrition information, but I don't think there's a fundamental reason LLMs can't eventually manage this use case, except perhaps the size of the needed weights being prohibitively large.

Per some people, LLMs of the future can do literally anything that's possible to do. They could create quantum computers powered by fusion power.

That has nothing to do with the question being asked, can you rely on an LLM today to help you track carbs as a diabetic?

This is very explicitly what the article is all about. Potential future LLMs are entirely irrelevant.