There are plenty of services such as Apple Pay (or equivalent tokenized services on other phones), 3D Secure, and/or PayPal that don't expose your PAN.
Europe is already essentially running on 3D Secure with 2FA. Becomes noticeable when buying from stores not having the EU as a significant market, usually American, which does not implement it. After the transaction is declined I'm forced to open my bank app and click the scary sounding "open my card for all internet purchases for 60 minutes" button.
That's not a problem, the problem is converting a user into a paying customer and the payment method is one serious friction point that Apple smoothed out so nicely. I am not concerned that I wouldn't receive the payment, I am concern that less people will bother going through the payment process.