The OP is broadly right. You now need to show ID to buy a SIM in many EU countries and beyond (e.g. Chile, Russia or Senegal). A copy of the ID is given to the state in order to link your identity to the SIM card. Even if you bought a prepaid SIM before this policy or law came in, when you top up the mobile provider may pressure you into paying online or by card instead of cash, so that your identity can be linked to the SIM through your payment.

I do wonder how long the US (or, for example, Finland) will remain a holdout in this regard.