This fails to acknowledge that synthesized noise can lack the detail and information in the original noise . When you watch a high-quality encode that includes the actual noise, there is a startling increase in resolution from seeing a still to seeing the video. The noise is effectively dancing over a signal, and at 24 fps the signal is still perfectly clear behind it. Whereas if you lossily encode a still that disca…
To illustrate the temporal aspect: consider a traditional film projector. Between every frame, we actually see complete darkness for a short time. We could call that darkness "noise", and if we were to linger on that moment, we'd see nothing of the original signal. But since our visual systems tend to temporally average things out to a degree, we barely even notice that flicker (https://en.wikipedia.org/wiki/Flicker_fusion_threshold). I suspect noise and grain are perceived in a similar way, where they become less pronounced compared to the stable parts of the signal/image.
Astrophotographers stack noisy images to obtain images with higher SNR. I think our brains do a bit of that too, and it doesn't mean we're hallucinating detail that isn't there; the recorded noise - over time - returns to the mean, and that mean represents a clearer representation of the actual signal (though not entirely, due to systematic/non-random noise, but that's often less significant).
Denoising algorithms that operate on individual frames don't have that context, so they will lose detail (or will try to compensate by guessing). AV1 doesn't specify a specific algorithm to use, so I suppose in theory, a smart algorithm could use the temporal context to preserve some additional detail.