Our 67 plate NX got the upgrade, we paid for it (£80) outside purchasing the vehicle as we didn't buy it locally. We were booked in that same week and had no problems and made the very antiquated system useable again, however this was before the world had its successive meltdowns so that may explain your delays.
The process is quite long so it had to be left for majority of the day and they had suggested doing it during a service, but that wasn't due for 9 months and the wife isn't that patient haha - maybe they cba with the labour time for £0 essentially.
Agreed that the 'physical' is misleading, you already have that bit in the car (hence being able to upgrade) and not like we have wonderful advancements in technology to allow rapid communication.
I would be one of those people who says 'I would like xyz done to the car as well (for a decent amount of money) and see if said back order magically resolves itself... 🤷♂️🤣