What a great prompt! Here are a few interesting off-label use cases I’ve used, imagined, or seen in the wild:
Greg McVerry, Ian O’Byrne, and I have integrated Hypothes.is into our digital/online commonplace books in different ways. Greg’s are embedded at https://jgregorymcverry.com/annotations, Ian discusses his process on his site, while mine show up as annotation or highlight posts.
I’ve not published the full idea yet, but I’ve spent some time contemplating using Hypothes.is as a blogging platform/CMS. It might require a bit of flexibility, but it generally has reasonable support for:

Writing posts with a reasonably full-featured text editor and the ability to edit and delete posts later;
HTML and markdown support;
Public and private posting as well as sharing content with other private groups;
The ability to reply to other websites;
The ability for others to comment on your posts natively;
A robust tagging functionality;
The ability to socially bookmark web pages (blank page notes);
An RSS feed;
The ability to share posts to other social platforms including meta data for Twitter cards;
Naturally, it’s very easy to use for writing short notes, creating highlights and annotations, and keeping track of what you’ve read;
It has a pseudo-social media functionality in that your public posts appear on a global timeline where people can read and interact with them.
It’s also opensource, so you can self-host, modify it, or add new features.

I have been personally using Hypothes.is to follow the public feed, several tag feeds, and several friends’ specific feeds as a discovery tool for finding interesting content to read.
And a final off-label use case that could be compelling, but which could have some better UI and integration would be to use Hypothes.is as an embeddable commenting system for one’s own website. It has in-line commenting in much the same way that Medium does, but the entire thing could likely be embedded into a comment section under a traditional blog post and be used in much the same way people use Disqus on blogs. I’ll note that in practice, I find Hypothes.is far faster than Disqus ever was. I’ve yet to see anyone offloading the commenting functionality of their blog this way, but I’d be willing to bet dollars to donuts that someone could hack it together as a simple iframe or via the API pretty quickly and with solid results.
And naturally I’m missing many, potentially including some I’ve thought about before. Maybe worth checking the old Hypothes.is tag in my digital notebook?
If people have others, I’m enamored to hear them.