Aside from the fact that, as you mention, you separate form and content, which is both wise and effective in most cases, you also have to consider the fact that you can write LaTeX on nearly every text editor (I say nearly because I usually prefer having syntax colouring on when coding a layout… but pretty much anything is fine for regular text). And dedicated editors usually have just one button, one that works when you click it – which is perfect for dummies like me. Word processors have so many buttons and menus everywhere, so many options to tamper with, and behave in such an unruly way that I feel like banging my head against the closest wall whenever forced to use them. Some of them are even evil enough to randomly swallow your footnotes (or is it just me they hate?).
If the alternative is MS Word, all documents require "advanced" typesetting. One can usually spot a document written in a word processor in about five seconds, mainly because of the default layout and of the horizontal and vertical spacing. As has been said by others above, as long as you define your own basic templates for most texts, writing a LaTeX document will basically require you to copy a file that contains the preamble / layout, or load a package you created for such use. This is not much of an effort and certainly does not take more time than using a word processor, in which most things cannot be automated.
Regarding automation, as has been said above, Bib(La)TeX does a great job at citations, and I don't know how I would manage to write anything if it weren't for it – writing up bibliographies yourself and making sure they are somewhat consistent is just awful, writing indexes would simply be out of the question. And you can use all sorts of default or custom commands for bits of text, with the advantage that you can redefine them at any time, should you need to. One can even automate most language and punctuation related things, and this really saves time for most languages.
That being said, I admit that I do not use LaTeX for everything. For one thing, I do not send my emails with an attached
.pdf file because most people would not read them, and it does not really make sense anyway except for very long or very formal emails (in which case I do use LaTeX). I do not use LaTeX syntax either when writing up to-do notes and lists of things, because I would never process them anyway and just read the text as it is (but then again, I usually write these by hand on a piece of paper). And I have some old text documents that I have been too lazy to convert, but that's definitely a mistake on my part.