Logs' purpose is to tell you what actually happened in the system. I don't think it is a good idea to use something that "hallucinates" to tell you what really happened.

LLM would be great to parse all that data, but I think you miss OP's point. AI can be useful to automate mundane jobs, i.e. jobs you can't get away from. OP's point in my view is verbose logs are noisey & difficult to parse, because you're logging everything unnecessarily. If you Log interesting things and mark them with context & logging levels, Then you can dive in as deep as you need, when you need. Why add complexity (& other hazards) of AI when you can fix the root of the problem first yourself.