I actually see a legitimate use case for it and helped add the actions version in a project where I'm a collaborator.
Quite a bit, certain bugs disappear after an update without us targeting it (partially because the logs get fudged a bit after going through dependencies, so sometimes multiple bugs have the same cause or it's actually a dependency issue that got fixed) and sometimes we forget about old feature requests.
The stale reminder doubles as a reminder for us to (re)consider working on the issue. When we know something probably isn't gonna get fixed suddenly, we apply a label to the issue. For enhancements that we'll definitely work on soon™, we apply help wanted. We've configured the action to ignore both. We also patrol notifications from stale to see if something shouldn't go stale. This is a medium-sized project so we can handle patrolling and IMO this helps us quite a bit.