For sure political innovation is a terribly slow process. I don't believe leveraging LLMs will have a direct observable effect on that until civilization <> AI digests for little while longer. Yes we could certainly discuss AI governance (governance by AI)

There are two other areas you would seem to point at. Firstly other technological innovation will have momentous effects, I will not name the buzzwords but you easily know from what by excluding AI/LLM. The second and far more interesting is what I will call political innovation which is orthogonal to technological development, which is totally driven by changes in consciousness. I think that often looks like a stepfunction, because I hardly see the needle moving there outside the generation-to-generation cultural noise.