You shouldn't have to re-pair anything moving it from one device to the other. If you wanted the remote to control the av volume that won't work not directly. Since the only device the roku remote controls the volume is the tv and only the tv. It is upto the tv to control the av receiver volume via hdmi-cec. Its a microphone and not a light.
I didn't think I'd have to re-pair either, but had no choice. The stick only shows up on one of the HDMI ports, where it hangs. I'm reasonably technologically adept--I built my computer, but this should be such a headache.
And Roku says that it doesn't provide phone support "because of the situation" which is just them being cheap. Everyone else had figured out how to provide support. Maybe time for an Amazon firestick.
Will make a new post out of this thread.