I was initially dreading that it would be something inefficient like the equation symbol selector in Word, but after viewing the video demo on their website and seeing the speed of typing aided by heavy use of shortcuts, I'm intrigued. I'll try it out someday!

TeXmacs is a great project, no doubt, but you have mentioned WYSIWYG as one of the advantages. This is the main reason I do not use TeXmacs to create documents (I do use it to create online lectures). You may like or dislike LaTeX/TeX (and the discussion is usually too emotionally charged for my taste) but the fact that it is a text format (not as verbose as, say, XML, at that) which is more or less standard is a deciding factor for many people, including myself. On a personal level, while I slightly dislike LaTeX style macros, I absolutely adore TeX's design (yes, including syntax). It is a matter of taste, of course. I am aware that TeXmacs can export LaTeX, it is not quite the same. LyX is another (better in my view) WYSIWYG option, if one is desired.

A TexMacs file can be opened up in any text editor. It's readable -- XML-like without quite being XML. Presumably, this can be used to work around some limitations of the WYSIWYG editor.

I think LyX's file format is not as well-designed.

Is there an equivalent of \NewCommand in TexMacs? I can't find anything by Googling.

TeXmacs has its own macro language. The equivalent of \newcommand is \assign together with \macro (yes, TeXmacs has proper first class macros, like any respectable language, e.g. Lisp). And macros arguments can be edited visually, here's an example: https://twitter.com/gnu_texmacs/status/1251554336842407938

you can check also the manual which comes with the program, in the menu Help->Manuals.

There is a good introduction in Chapter 12 of The Jolly Writer: https://www.scypress.com/book_info.html