I think this is the other way around: conservation laws come from the instant connections entanglement represents.

All the emission-flight-absorption processes we can observe as happening at the speed of light are, at the same time, instant action/reaction events for the massless quanta involved. From their perspective, time does not exist, so they don't go anywhere, or loose any energy, because they can't change or evolve. So they have no other choice than to comply with conservation rules.

The universe runs on entanglement under the hood. Any entity is either massless, or its perturbations propagate through the different fields that exist at light speed. Proper time is zero in these cases.

We wonder how conservation rules are enforced at a distance, which communication mechanism makes it possible. The answer is that there's no "at a distance" for massless quanta, so there's no need for a specific mechanism to communicate in space or time from their POV.

The conservation rules we observe are a direct consequence of entanglement, not the other way around.