I find the interface is less "busy" as a result of giving up some of the constraints of WYSIWYG (e.g. a simple line to mark page breaks rather than drawing a page on the screen). Interestingly older versions of Word (in the Windows 3.1 era) were similar.

Styles are more emphasized - the UI will nudge you away from manually changing the font size of one line and towards defining styles for different things. Word has that functionality but it's not quite front-and-center in the same way.

I use LyX for non-maths. It renders nice-looking PDFs (I use it for my CV (well these days I use Kile instead, but same principle)). It's a pretty marginal choice though honestly.

I like the look of a LaTeX document better than that of a Word document by a mile.

You can probably get a Word document to look great as well but in LaTeX it happens by default. It actually provides you proper typographical advantages without you needing to know anything about them.

Worry about writing and not about formatting frees up your time to do what matters.

LyX can also integrate with knitr for embedded R code in your document. That can help enable reproducible research documents, which is not strictly math related: pretty much anything with data and graphs can benefit from that