I am facing this right now as well. I think it would be a good idea for sites to be able to have an e.g. moderators@siteurl email address, so that people who are having trouble logging in or don’t even have an account can still reach out and have their queries handled through the same group inbox they use for handling flags, moderating discussions, and helping members with their accounts.
That email address could then be listed on the about page and in the TOS and privacy policy, for moderator related inquiries.
You’d still need an email address external to the site so you can be reached in case your site goes down or has some serious technical problem.
There is a risk of spam but that’s what automatic spam flagging is for! 