> In your "time complexity is a downstream requirement" example, which is a great one, I think you would prefer to have well-maintained written documentation of that criterion that lives outside of the procedural code itself, would you not? How much attention that doc gets is a matter of process and preference, but I'm advocating it should get more (spec-first).

That is a huge mixed bag. It helps to have an high level overview of an algorithm. If you want to be very accurate about an algorithm, then that documentation is potentially harder to digest then the actual code. I personally don't even know how to express an sophisticated algo in natural language without falling back to pseudo code. Then you also have to verify a purely natural language defined algo with a very slow feedback loop (agentic PR cycle) against a test. Which seems to be a guarantee for myself to get sloppy because it's annoying.

There are a lot of reasons to theorize about algos in spoken or written natural language. For me it's questionable why you'd prefer the natural language to be the reference implementation when all you want is the code. That only makes sense if you never want to look at code.