I personally hate it when a bot closes an issue I wrote. What's the point of closing unresolved issues? Just assign them a label (it could be a "stale" label like some projects do). Otherwise it just feels like hiding your mess under the bed. Other sorting tools can provide the same list as automatically closing bugs would achieve. The opposite isn't true, unless assigning a specific label when manually closing an issue.
I don't think closing such bugs is "feed a human desire to hit "inbox zero"" even with that you'll never get there. From my perspective it is all about not losing track of important issues. Having bots close tickets makes sure that only tickets are opened are ones that someone cares about. There are tickets that are from 2013, a lot changed since then, they might no longer be relevant anymore.