Designed c. 2005, the extension is one of the critical tools that helps us to deal with problematic cases of abuse such as sock puppetry, vandalism and spam (some history here). As time went by, the needs of the projects increased, and as we can see in the CheckUser work board, the bugs accumulated without being resolved, primarily because its code, albeit old, also seems hard for developers to read and work with (refer to T132892: CheckUser UI revamp and its related tasks, as well as the work board I've linked above).
The lack of an active maintainer for the Extension in question lowers development productivity in this area (i.e.: bug resolution, testing and extension development ex Phabricator). To resolve this issues, I think we need to think about overhauling the CheckUser extension. That overhaul should also be an opportunity for us to make the extension work with all the new features and code MediaWiki has at its current state. We can also take this opportunity to gather opinions from CheckUsers on which new functions the new CheckUser extension should have, etc.
I think that we can start this big task by making a UI revamp, and later explore if new features could be added to the extension as well. If someone or various people could also volunteer to be active maintainers of the extension, that'd also be fantastic.
I'd like to thank all of those who created the extension and have worked with it so far.
Sorry if the format is wrong or I missed something. It's the first RFC I've filed here. Let me know if there's something that needs fixing and I'll try to do that.
Edit: since rewritting from scratch is a bad option according to experienced developers below, modified some parts of the intro as well.