In the field of AI
wishful mnemonics is the rule, arguments about prescription are of limited value.
CoT scratch space extends LLMs from DLOGTIME-UNIFORM TC0 to PTIME with polynomial sized scratch space.
https://arxiv.org/abs/2502.02393
Yes prompt engineering is probably better though of as prompt augmentation or stearing.
But the systems identification problem and Rice's theorm rigorously debunk the above links core claims.
It is a craft that can improve domain specificity and usefulness.
All models are wrong (even formalized engineering ones), but some are useful.
The price one has to pay when resorting to what is fundamentally compression as PAC Learning is, that it is fundamentally unstable under perturbations.
You are basically searching through a hay stack with a magnet, and making sure that at least one of the needles you find is the correct one is a symantic property. Guiding the approximate retrieval process to improve your results will always be a craft.
The snake oil is mostly on the side that claims that unrestricted natural language is a possibility. We still only have NLP, and true human level NLU is still thought to be beyond the limits of computation IMHO.
Thus prompt augmentation is a consequence of the argument that link was trying to make.