There are probably some people who see a 3k bug report number and think that, but realistically tons of projects have thousands of open tickets for any number of things from legitimate bugs to duplicates to actual user questions. Linux, projects like LLVM, etc. It's natural when you have a project that is in active every-day use by literally thousands and thousands of people. Nixpkgs is simply a big project! But the actual numbers might tell another story.
For reference, the LLVM bug tracker has exactly ten thousand open bugs as of this writing, and I assume that number is only so perfectly rounded because Bugzilla search refuses to return any more results in a single page that already brings scrolling in Chrome to its knees. You won't find any lack of praise for LLVM's high quality and extensible nature, though -- they can all be true at once!
The nixpkgs label tracker isn't highly accurate since auto-labeling only started earlier as of this year, but as of this writing, of the 3k open issues, about 500 of them are directly marked as bugs, while 41 are marked as regressions. There are 200 enhancement requests, and 50 open packaging requests. So of 3,300 bugs, about 800 can be quickly classified, and about half of those are actual bugs. This is a very ballpark number (GitHub search doesn't allow XOR). Considering nixpkgs is literally shipping thousands of other software projects, I think this is pretty good -- even though I wouldn't argue it could be cleanly extrapolated to the whole set of bugs, because of a long tail of old bugs.
In terms of cadence, over the last month there were ~466 new PRs, and ~1,600 merged PRs. ~220 closed issues vs 215 new ones. This is done by nearly 350 contributors. I would think this is also very good and the sign of a healthy project with hundreds of active developers. IMO, if just a raw number of "3,000 open github issues" has to mean anything ("this software is unstable"), then these numbers have to mean something too. It's just that GitHub doesn't "helpfully" post them on every single page concerning your project...
But I do agree we should have better mechanisms for discovery and keeping things clean. Duplicates certainly happen and are annoying, and nobody likes drudging through 1,000 of the oldest open reports to close old stuff, etc. Some of this is also limited by GitHub and other things, unfortunately.
Personally as a developer (not a user!), I think bots that close old tickets are often very annoying (to everyone) and rarely do much other than feed a human desire to hit "inbox zero", but this desire is not (to my knowledge) based on any actual scientific criteria that leads to better software development or happier, better cared for users. It is more a way of externalizing a deep human desire for "cleanliness" and using it as a yardstick for "quality" rather than evaluating the numbers for yourself. You can also find tons of 0-issue repositories on GitHub, but this doesn't mean they're actually good, or they do what you want -- and I doubt most of them have as much momentum as we do.