I think you're glossing a bit over the word "intention". It's certainly easy for any competent manager to communicate instructions or requirements in writing. What's hard is communicating the full scope of their intentions, including things like:

* This bit is confusing to me even as I say it - I want to keep it in mind as we move forwards in case we're thinking about it wrong.

* This requirement is really annoying and I'd love to find a way to get rid of it.

* This part is super super urgent, and if we find a way to do it faster without too many other costs we should rework the plan.

You can't "just" write these things down, both because some requirements aren't so annoying you can come out and explicitly say it and because too many parenthetical clauses start to make a document impossible to read. If they're not communicated nonverbally it's hard to communicate them at all.