If later it turns out this was a sim swapping attack you can verify if the clerk entered a valid document ID. He can’t do that without having been presented a proper document, so you can tell if he checked.
I wasn't sure how would you solve the problem of verifying the ID card without showing the previously recorded number to the clerk. But simply requiring to every time just punch in the ID (and maybe scan the whole card to check the photo later) could work - if the system only returns a big OK or BAD signal.
Currently here, in Hungary, the clerks just photocopy the IDs though. And there was a big scandal a few years ago (in connection to the ISIL/ISIS attacks in EU) about some groups obtaining hundreds of thousands of SIMs for just a few names.
A recovery code snail-mailed/e-mailed to the account holder when they first open the account is the correct way to go, and if they can't provide it they need to go through a lengthy process where many factors are used to authenticate them (verify their physical address, verify their ID, ask to confirm last call records, billing details, etc).