For one, it eliminates a class of merge conflict that arises strictly from text formatting.
I always liked the idea of storing code in abstraction, especially editors supported edit-time formatting. I enjoy working on other people's code, but I don't think anybody likes the tedium of complying with style guides, especially ones that are enforced at the SCM level, which adds friction to creating even local, temporary revisions. This kind of thing would obviate that. That's why I also appreciate strict and deterministic systems like rustfmt. Unison goes a little further, which is neat but I think they're struggling getting adoption because of that, even though I'm pretty sure they've got some better tooling for working outside the whole ecosystem. These decoupled tools are probably a good way to go.
I was messing around with a file-less paradigm that would present a source tree in arbitrary ways, like just showing a individual functions, so you have the things you're working on co-located rather than switching between files. Kind of like the old VB IDE.
From that perspective alone the session would be important meta information that could be used to determine the rationale of a commit - right from the intent (prompt) to what the harness (Claude code etc) made of it. So there is more value in keeping it even in your second scenario
If you do proper software development (planing, spec, task breakdown, test case spec, implementation, unit test, acceptance test, ...) implementation is just a single step and the generated artifact is the source code. And that's what needs to be checked in. All the other artifacts are usually stored elsewhere.
If you do spec and planing with AI, you should also commit the outcome and maybe also the prompt and session (like a meeting note on a spec meeting). But it's a different artifact then.
But if you skip all the steps and put your idea directly to an coding agent in the hope that the result is a final, tested and production ready software, you should absolutely commit the whole chat session (or at least make the AI create a summary of it).
"Beekeeper trains a bumblebee queen to use a protective cap in less than 24 hours. This protects the colony from hornets and similar threats."
https://x.com/MyLordBebo/status/2033115074982813727?s=20