I'll bite, I think Turing completeness is relevant in that it has to be used to informally argue via the Church-Turing thesis that biological intelligence cannot exceed the power or expressivity of formal neural network models. It thus is a good counterargument to stochastic parrot dismissals of neural net based AI such as LLMs, which really are still black boxes. The issue is not simply "So you think that humans are as powerful as LaTeX (or vice versa), ha ha how absurd!"