I 100% agree with all of this except for short emails. Short emails encourage less thinking.
I put my conclusion right up top for the tl;dr crowd, but I always SHOW MY WORK, not because I think others will read it (they won't) but because 1) thinking (and writing) through an email request or response helps me to anticipate and proactively answer questions and 2) primarily because documenting the "head space" I've invested time in creating helps me quickly get back to it when someone asks about the topic days, weeks, or months later.
People who have to switch between complex, abstract topics should not feel bad about writing long emails. Want to disagree with my tl;dr summary? Be my guest, but woe unto you if you haven't read the supporting detail.