The fact that getting a formal spec is impossible is precisely why you need to hire a developer with a big salary and generous benefits.
The formal spec lives only in the developer's head. It's the only way.
Does an LLM coding agent provide any value here?
Hardly. It's just an excuse for the developer to waste time futzing around "coding" when what they're really paid to do is cram that ineffable but very much important formal spec into their heads.