Inboxes only work if you trust how they’re drained, but it’s hard to keep them that way. It’s even harder to do this if a single conceptual inbox (e.g. “things to read”) is spread across many different places.
Reliable inboxes require that departure rates >= arrival rates, but if an inbox is spread across many places, it’s difficult to see and manage those rates (e.g. by dropping or deferring items).
One solution may be to create virtual inboxes which present a unified interface to several “places” where that conceptual inbox’s items live; see My implementation of a reading inbox.