The serial number is likely embedded in the wireless communications initial handshake protocol to insure that your cellphone establishes communications only with your streamer, and not some other streamer device that happens to be in close proximity.
Same thing happens between your right and left hearing aids when they initially establish communications with each other to coordinate tasks such as volume up, volume down, program change up, program change down.
Without establishing communication to that one specific device, bad things might happen. For example if you turn up your hearing aid volume in a crowd of people, it might turn up the volume for others in that crowd.