This document is already large and complex and the source of many configuration mistakes. I worry including basic information like this could cause more harm than good, by making the document even larger and making it easy to miss something important.

We've never seen other users encounter difficulty with this, the document already warns that this setup is "Hard", the install guide warns about "Level Requirements", etc. The need to put the private key on the client should be self-evident to anyone who is configuring an SSH server.