I report the fraud to my card company. The card company reverses the charges and purses action against the fraudster if possible. The card company then tells me that because contracts made over the phone are null and void, using the credit card to make purchases over the phone is not allowed and doing it again will result in my account being closed or a penalty fee being assessed.

The long term effect may be that credit card companies stop supporting remote transactions that don't use biometrics+attestation or the physical card.