I've spent a lot of time in both Word and LaTeX writing papers and reports in grad school, and nowadays, strictly use LaTeX. I feel like the author missed some crucial elements as to why people use the latter. First, references, cross-references, and citations. These are all shockingly simple in LaTeX. \ref or \cite is all you have to think about to cite papers or reference figures, tables, etc. In Word, I have used Mendeley's citation system, and the built in cross reference system to the same task, but when it comes to the editing process between multiple people and having different files sent around, it invariably breaks, leading to hours of extra work either doing it manually (have fun updating figure numbers if you add another one, or citation superscript), or reinserting all the necessary cross references. With a LaTeX file, this is pretty hard to break.

Secondly, LaTeX handles figures 10000x better than Word, in that you just let it figure out placement inline. Captions are as simple as possible. Meanwhile, have you ever had that Word document with 10 figures in which you move one inline image, and every figure jumps to a different page, leading to spam clicking Ctrl+z? Or how about adding figure captions? Inline you have to use the caption tool, which isn't fantastic and often creates a text box that isn't strictly tied to the figure. The method I found best was just to have another document simply for figures and write the captions in regular text. This both looks bad, and during the editing process, requires you to switch between files to keep track of the figures that are being referenced in the text. Additionally, automatic figure numbering depends on where the figure anchor is, often leading to improper numbering. Again, referencing figures by number in Word is a nightmare that LaTeX handles amazingly.

Third, I agree, setting up LaTeX on a machine isn't fun, and I have always been bad at it. However, I don't do it anymore. ShareLaTeX has solved all of those problems for me. All packages are available, you don't have the funny "compile three times to get reference numbering correct", it's amazing at collaboration with both git-like diffs as well as Word-like track changes/commenting system, and has tons of templates so the pain of setting up your document's preamble is done for you.

One tip I have is if someone you work with doesn't know LaTeX and can't be convinced to learn it, still write in LaTeX, compile to pdf, and use Acrobat to convert to Word. That works surprisingly well. The Lyx version conversion does not work nearly as well. I can't say I've tried pandoc though, I would like to try that next.