A few experiments further, it seems that Word has indeed decided I don't want to see the visible characteristics of the Hyperlink style on my cross-references … even though the Font panel says they are being applied! [no screenshot, because corporate policies block Dropbox; I'll try and add one later]

I'm not impressed. I think I'm old enough to decide for myself what visible clues I want to give my readers. Also, if examining formats tells me certain properties are set then those are the properties the document should display.