People flag posts when they want to delete things, so that would make those private messages visible to moderators. We have some content analysis tool running too, so if a post gets auto-flagged, it might suddenly become visible.
I’ve also had bad experiences in the past from giving people too much access. One moderator was using his position to build a clone of the site on another domain. Another person who had too much access once deleted a lot of content without warning. For me, it’s more stress than it’s worth.
At the moment, I send a webhook into a cloud function whenever there is something to moderate. The function pings a channel on Slack, so I can usually take care of common problems from my phone within 60 seconds of the incident.