This is a loaded question. Is there a better way? Maybe. It is almost certainly not any easier, though. Likely takes longer and requires as much investment from the reviewers as it does from the authors.

I confess I'm fond of Literate Programming for this, though, I have never tried introducing it in a company. My hunch is it would take too long. By far.

Even documented software often takes too long. Same reason you don't plot out how you are going to win a ballgame. Outside of "score more points than you allow", the plans are almost all exploratory and reactive. Solidifying that into a document is dangerously slow.