Does Word not default to switching all typefaces - header, footer, etc.? If so, IMO that’s a bad design that violates the principle of least surprise.

Word works very well without surprises if you have learned how to use templating and proper headers - the semantics. Big if!

I will claim most people still just do selections and change font/weight.

So what is good design? Something which enforces our geeky ideas of a base font? Or something which let people easily do what they want to do and get work done? Who should get the least amount of surprise?

Design is taste. Taste leads to principles. Principles makes things easy. Design is also compromise. Compromise is hard. Design is hard.

While it is possible to use "semantic" styling and page layouts and templates in Word, I would argue that Word owes its popularity to the fact that no user is surprised when they select text, change the font, it does not change it anywhere else.

It is one of the tools that popularised "WYSIWYG" as an approach, and as we know from many other tools, you lose something when you adopt a tool like that.

Now, I'd always recommend and use a TeX-based document layout system (but despite my huge respect for DEK, not Computer Modern family of fonts, even for mathematics), but many struggle with non-visual document entry: it is no surprise scientific community is the only one which standardized on it since inputting mathematics visually is a PITA.