I've tried to hit the right balance between being thorough and readable. There are at least ten ways of connecting mappings with modes, and double that if you care about recursive definitions. That's fine for a reference manual, such as :help, but the detail can seem daunting to the amateur user.
It's more than likely that I haven't achieved this balance in places, and if so I welcome help to clarify them.
Lastly, as I wrote on the index page of the site, this is still a draft. I published it so I could get feedback. :-)
:w is mentioned as a footnote because :up is more sensible in the general case, as it preserves file timestamps and saves needless disk access, the latter being particularly useful when dealing with larger buffers or working over a slow link. If somebody wants a quick answer to the question, they can just look at the Solution. If they want to understand how saving works, and its how it relates to existing mental models they have of text editors, the Discussion elaborates.
This is in contrast to the "cheatsheet" approach, which does exactly what you suggest. It gives a single cryptic command, then moves on to the next example. This may be sufficient for you and I, but newer users would prefer a more cohesive explanation.
Oh, and the "Needless Comment Form" was added after multiple readers requested it. Apparently people find it easier than cloning the Git repository and submitting a patch. ;-)