About the 10 words to cut listed in your post, a few are debatable, but the got to be cut in "I got up this morning" seems to me completely off, it seems to me perfectly correct, and "wake" has a different meaning from "get up".
I knew before checking it out that 'just' would be on the list, I've always used it liberally and only recently focused on cutting it from my writing.
It [just] feels natural and I'm not sure why. When saying it out loud it helps reinforce something naturally and no-one really notices, but when plastered all over writing it really pops out and shows that it's not all too useful.
For example the author complains that some words reflect "the way you talk" or are too "casual".
Well, sure, and? That may be entirely appropriate depending on the context.
Are we talking journalism? Technical writing? Casual blogging? Fiction?
Honestly, if there's one thing I've learned about rules for writing, it's that there's no one set of rules for writing.