In my 30 years of software development, maybe 5 of them were in places were getting people to provide a formal spec was ever an option.
It's also irrelevant if LLM's can follow them - the way I use Claude Code is to have it get things roughly working, supply test cases showing where it fails, then review and clean up the code or go additional rounds with more test cases.
That's not much different to how I work with more junior engineers, who are slower and not all that much less error-prone, though the errors are different in character.
If you can't improve coding speed with LLM's, maybe your style of working just isn't amenable to it, or maybe you don't know the tooling well enough - for me it's sped things up significantly.
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.
It works just fine to use an LLM coding agent in cases like this, but you need to be aware of what you're actually trying to do with them and be specific instead of assuming they'll magic up the spec from thin air.
It's also irrelevant if LLM's can follow them - the way I use Claude Code is to have it get things roughly working, supply test cases showing where it fails, then review and clean up the code or go additional rounds with more test cases.
That's not much different to how I work with more junior engineers, who are slower and not all that much less error-prone, though the errors are different in character.
If you can't improve coding speed with LLM's, maybe your style of working just isn't amenable to it, or maybe you don't know the tooling well enough - for me it's sped things up significantly.