The end here reminds me of "The Log: Real-time data's unifying abstraction" [0], which has unfortunately had a bit of link-rot since 2013.

One complication in this approach involves access-windows: What if my system is only supposed to be seeing stuff that happened during two separate weeks in the year, because those are the spans when it was subscribed or authorized?

So the data-host would need to maintain a concept of "connection history" for other services, and also use that to filter/modify its real event stream, inserting artificial "initial state" roll-ups of events that happened in dark periods.

[0] https://news.ycombinator.com/item?id=6916557