In fact I don't think I've every been on an elevator that had music.
Google sez: Music for Airports was installed at the Marine Air Terminal of New York's LaGuardia Airport for a brief period during the 1980s.
Elevator music may no longer be a thing, but apparently, airport music still is:
https://www.youtube.com/watch?v=Km0h6Ix3Zcs
In fact I don't think I've every been on an elevator that had music.