That's right, but it doesn't add up to what you said about spacetime being saturated with 'world-branching' events.
While the decay wave is propagating, for instance, nothing's decohering. It's only when it reaches the critically unstable system of the detector that that happens.
It's only when it reaches the critically unstable system of the detector that that happens.
There is no single moment like that. if the distance from the atom to the detector is r and we prepare the atom at time 0, the interaction between the atom/field states and the detector states (i.e. decoherence) starts at the time c/r and continues on.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.