It seems like you're imagining a different situation than I am. I'm talking about a large volume of outside email, the equivalent of fan mail, essentially. We have other methods of communication for internal stuff, like Slack.

I stand by my original assertion that your request for attention doesn't create an obligation to give any to you, though. I think the cultural norms around it (ie, give attention when asked) make sense at small scales, but break once you cross a certain threshold of people wanting attention.