Card verification via sms

Yes, the bank that issued the card picks the method they use for verification. I’ve provided additional information to help with the understanding of the issue you’re facing. Not sure it’ll help the bank though. 

>>Adding additional verification

A card issuer can decide whether a credit or debit card requires additional verification. Depending on what’s offered by the card issuer, the user may be able to choose between different options for additional verification, such as a text message, email, customer service call or a method in an approved third-party app to complete the verification. For text messages or email, the user selects from contact information the issuer has on file. A code is sent, which must be entered into Apple Wallet, Settings or the Apple Watch app. For customer service or verification using an app, the issuer performs their own communication process.<<

Adding credit or debit cards to Apple Pay - Apple Support

Card provisioning security overview - Apple Support

You’ll need to escalate your issue with the bank. If bank support will talk to their own IT department, I’m sure the bank will figure out the verification is their procedure, no Apples.

I’ll link to the Apple document that explains the whole process for provisioning the card.

Card provisioning security overview - Apple Support

Google Pays uses different technology and I can’t comment on their processes and procedures.

The method for deciding which verification method to use is >Depending on what’s offered by the card issuer.<< The card issuer picks the method. Apple, device and user play no role in picking the verification method. Only the bank that issued the card picks verification method. Have you talked to the support team at the bank? You can contact them by calling the phone number on the back of the card.