The obvious way to do this is that you need to physically attach the bank card in order to authorize a new vendor. So then when you sign up for Google Pay or Paypal or what have you, you need to get out your card -- which is good. You can't steal a physical card by breaching some other merchant it was used at.

From then your Google Pay account is authorized to initiate charges until you tell your bank otherwise and you don't need the card again unless you want to sign up for Venmo etc.

And it makes things easy if someone steals your phone, because you just sign into the payment processor and deauthorize the device or, if they've already changed your password etc., sign into (or go to) the bank and deauthorize the payment processor.