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.