Today, when an org receives an event and they don't have any integrations linked to the event type, the event is recorded into the Event Log and nothing else happens (no outgoing notifications). Notifications admins most likely miss it. They might even be unaware that the event type exists.
 
What if, tomorrow, we helped the Notifications admins be aware of the notifications their org missed, by sending them an email notification about it?
 

Your organization received 123 events from service XYZ over the past 7 days, but no notifications were sent because you don't have any integrations linked to event type ABC. Click here to learn how to be notified about these events.

 
This could be done on a regular basis (daily, weekly...) and rely on a new event type (under Notifications) which could be subscribed by default, while allowing users to unsubscribe. This way, all admins would receive the first email about missed notifications, and then decide whether they want to continue receiving it or not.
 
The email would likely look like a digest, listing notifications they missed from all services in a single email.
 
Optionally, we could notify admins only once per event type and avoid repeating the same content every day/week/...