I would like to think that pg_hint_plan is designed in such a way that any hint it accepts must be a valid plan for the query. I’m quite confident that schemes with this property that can also express high quality plans are possible and not even excessively complicated.

This is not to say that it’s possible to genetically verify that a proposed algorithm does what you want it to — that would be undecidable or NP-hard or co-NP-hard depending on how you formulate the question.

I wouldn't be very excited about adding a 4B param model to my database deployment, but using this kind of approach while testing an app to identify query plans where Postgres is leaving performance on the table seems valuable without much risk.