All I know is that the stuff in roaming generally follows you around on domain logins. So if you're bouncing around on corporate computers with the same standard set of apps installed, if they save their stuff in roaming they can retrieve it anywhere you log in.

Which can be a blessing and a curse because once roaming fills up with all sorts of crap your logins on new computers take forever as the network has to transfer X gigabytes of stuff in roaming to that PC.

You’re right that that’s extremely unambiguous, but I still don’t love the idea that users don’t get to decide what’s in $HOME, like, maybe we could call it “$STORAGE_FOR_RANDOM_BULLSHIT” instead?

That's basically what $HOME is is used for in UNIX: a place for applications to store user-specific files, including user data and user files.

https://www.linfo.org/home_directory.html

If anything in computing conventions implies “user space” it’s a global variable named HOME. And it makes sense that there should be a $STORAGE_FOR_RANDOM_BULLSHIT location too - but maybe not the same place?

UNIX, and afterwards Unix-like OSes, were designed as multi-user operating systems that supported individual user accounts. Each user needs to store it's data, and there's a convenient place to store it: it's $HOME directory. That's how things have been designed and have been working for close to half a century.

Some newer specs such as Freedesktop's directory specification build upon the UNIX standard and Unix-like tradition, but the truth of the matter is that there aren't that many reasons to break away from this practice.