I don't understand this mindset. We have all experienced that LLMs can produce words never spoken before. Thus there is recombination of knowledge at play. We might not be satisfied with the depth/complexity of the combination, but there isn't any reason to believe something fundamental is missing. Given more compute and enough recursiveness we should be able to reach any kind of result from the LLM.
The linked article says that LLMs are like a collection of vector programs. It has always been my thinking that computations in vector space are easy to make turing complete if we just have an eigenvector representation figured out.