India's largest state bank (SBI) has somewhat moved away from just using SMS, their debit card now supports 2FA using their app and their credit cards now support 2FA over app, E-mail and SMS. Though I think RBI regulation still require a 2FA for all online domestic transactions.
The regulations require it to be enabled by default afaik. SBI (I don't have experience with other banks) allows you to turn off 2FA for different classes of transactions. It's hidden away in the settings on their legacy web interface.