Europe is not just EU or Westen Europe. The system the op is talking about iirc is only for free parking, so it’s not even an alternative to a meter. It’s an alternative to a meter maid making rounds chalking wheels or scanning license plates.
I definitely rented a car in Switzerland before pandemic that did not have the disk and I had to buy it at some tourist info center.
I think every car in Europe has this parking clock/disk.
If you do not have the clock, then piece of paper and written time is also OK.