Right, but the genius was in understanding that the dynamics of a system under PID control are predictable and described by differential equations. Are there examples of LLMs correctly identifying that a specific mathematical model applies and is appropriate for a problem?
And it's cheating if you give it a problem from a math textbook they have overfit on.
For a very early example:
https://en.wikipedia.org/wiki/Centrifugal_governor
It's hard to separate out the P, I and D from a mechanical implementation but they're all there in some form.