> ⇒ this may be useful for some workloads, but even then, can you afford to spend hours every now and then to update your 4B model to ensure it still picks a good query plan?

I think this would be likely comparable to a scheduled backup, so I think it would be an acceptable maintenance window. However, deterministic algorithms would likely beat re-training (or re-fine-tuning) the model. For example, one could analyze actual distributions or whatever (instead of assuming uniform), and then some plans would automatically be eliminated.

Imo a good thought experiment is to look at places that are hyper-optimized, like compilers. Would LLMs bring anything to the table (architecturally or performance-wise) to a piece of software that has been carefully crafted for decades? (Methinks no.)

The Postgres query planner has had to operate, for those same decades, in a much more realtime-sensitive and restricted environment than compilers. It can only draw its conclusions from summary statistics on tables in isolation, not on their relationships with each other (and even less so when filters are involved). For many cases this is fine! For many others it isn't.