do people really have this problem? I never remember being bombarded by a single source (be it a person or a service), email becomes a burden because there are many sources and the level of urgency is alternating even for the same source through time
Yeah I manage that by treating all mail as low priority and every chat as high priority. People chatting for spam or to bring attention to a low priority inbox gets told to send an email. This way I'm sure not to miss critical messages without relying on pepople self tagging
I would think this could be a real situation if you have a problem customer (read: demands more than their SLA) and you're not ruthless/effective in your communication.
Sometimes not responding in those situations can lead to better outcomes than replying in haste or frustration.