>Whilst writing this I looked around to see why people think it’s still a good thing to use, say, Chrome or Firefox instead of IE or Edge, and a lot of the reasons can best be termed “tenuous.”
As you note, IE is only cross-platform in the Microsoft meaning of the term: it runs on more than one version of Windows. We use more things that don't and can't run Windows at all now, and if you want a consistent Web experience then you want a browser that runs on almost all the things.
And then there are those web Office apps you mention. Microsoft history has their browser deliberately incompatible with other vendors' services, and their services deliberately incompatible with other vendors' browsers. They can't do the latter when their browser is a minority share without harming the prospects of their services offering. So even if you use Office 363 on Windows it's best to do so from Chrome to preserve your option to do so.
These reasons aren't "tenuous".