I think it can do more than the wave only events we know of (superposition, entanglement, and tunneling).
If the quantum field doesn't care about spatial distance, does that mean every unobserved quantum wave is already everywhere throughout the quantum field? Does it explain spooky action at a distance and the delayed choice quantum eraser?
I think we are going to find the Quantum Field is a bit like the internet cloud. All Quantum waves have access to it.
Does a quantum wave, that is destined to decohere, behave differently than one that isn't?
Decay of Coherence is something that can happen to decoherent particles. Coherent matter-waves do not decay.
The reason decoherence can be predestined is because the quantum field is everywhere and already knows of the decoherece events.
Quantum waves are not physical, they are not using anything spatial. The quantum field can influence the trajectory, but it can't make it tunnel or be in superposition. Unobserved waves do not travel in spatial dimensions.
The delayed choice quantum eraser demonstrates a particle of a pair landing on its final panel first, knowing if it's entangled brother will decohere in its path.