I think there's a misunderstanding here. If the customer mistypes the IBAN account number, the bank (website, app etc) will automatically reject it as invalid immediately, he won't have to deal with the customer service.

Yes, but the misunderstanding is on your side.

This is overly simplified so not entirely accurate, but if 100 customers typo their destination IBAN the modulo 97 checksum will probably let 3 of them through.

Wikipedia says that "where used, IBANs have reduced trans-national money transfer errors to under 0.1% of total payments", although there's no source for the claim.

0.1% of total payments, i.e 1 in 1000 payments. That’s not 0.1% of typos but all payments.