I can speak from a production standpoint. LaTeX can be a decent back end for an XML workflow, such as used by Scribe, which integrates Word templates, an XML database, Indesign (ID), and so on. The elements of layout and typography that you mention are a part of a greater picture. LaTeX typesets equations better than ID or Word. You can do equivalent things in LaTeX and ID, but the time and cost will differ, depending on the application. That triangle of time, cost, and quality can inform standards of beauty.
I started using LaTeX seriously when writing my thesis for my second master's degree. Way before that I had used TeX a little with my undergrad CS program on SysVr4 Unix. I needed to hyphenate English, German, Latin, and Greek. Word c. 2004 was still a mess with that. I got everything to work properly in LaTeX, much better than Word and EndNotes. Word has improved a little with hyphenation, but remains inferior. ID has a few options but it is neither as flexible nor as automatic as LaTeX. So if beauty means handling multiple languages well in the body text, bibliography, and footnotes, LaTeX is best.
I first designed the specs for Law and Gospel: How to Read and Apply the Bible (2010) using LaTeX, then the designer set up an equivalent in ID. Margin notes worked better in LaTeX than using the anchor mechanism in ID. There was a lot more human fiddling with the equivalent layout in ID. LaTeX automates a ton of features that you can set up in a template, then guarantee consistency and beauty thereafter.
ID is better at publishing on a grid and magically adjusting leading, character and word spacing across frames of text. Using microtype is very manual by comparison via
\textls and the
Spacing environment. But one still has to tweak the rules for individual paragraphs at times in ID.
The page ship out in LaTeX is different. It can do some complex things procedurally that would take longer to do in ID and be less precise and consistent, in my experience. TeX kind of imitates a Linotype hot metal press in the way it constructs pages. That has a certain beauty to it.
In LaTeX, if you use microtype and you start messing with leading, tracking, etc., you have to be very careful that you don't get unwanted page breaks or reflow when using widow and orphan control, which itself has multiple implementations. Furthermore, updating your TeX distro can cause a reflow. I saw this when I typeset my book, Breath of God, Yet Work of Man (2019) using LaTeX. That detracts from the beauty when "done" needs to be corrected and reprinted.
I typeset several books using Word because it allowed the publisher to use a template and outsource the work. That was nothing short of ugly. Even the idea of setting up running heads can be a chore because Word tries to think for you. You have to set up odd versus even headers with a different first page and ensure that the first page is odd. You have to pay super careful attention to the section links and set them up in order without any changes after they are finalized, else the links can break and your numbering is fried. Doing the equivalent in ID and LaTeX is a snap.
In Word you can play a little with spacing and leading, but it's an unstable mess and tends to reflow especially when using footnotes. Moreover, reflow can happen each time you open the document. Unwanted white space is hard to mitigate. Fixing that can take much time.
LaTeX and ID are of similar power and each is good for specific cases. LaTeX has as-yet rivaled power in automation of references, bibliographies, indexes, TOC, etc. The fact that so many design elements can be generated consistently and accurately adds to the beauty.