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This already exists tooThe fraud resolution on my Visa card[1] required me to:
1. call the merchant that charged the fraudulent charge, and attempt to get them to void it. This was literally as pointless as it sounds.
2. Receive a specific form that could only be sent by snail mail or fax. The sending end absolutely refused to send it over email. Thankfully my building has a fax machine, and my building manager has common sense, and allowed me to borrow it. The fax service we use (because who uses fax?) turns faxes into — you guessed it — emails. Of course, at the bottom of the received fax is "H:\SharedDocs\Stuff\More Stuff\TheForm.pdf".
3. Fill it out, scan it back into a computer, fax the PDF back. (I could have also snail mailed it back.)
4. Receive a confirmation over snail mail, noting that it will be resolved sometime in the next 6 months.
I never lost possession of my card, and the merchant who charged the card was able to confirm that the "card" was presented at the time of purchase (it was made physically, in a store) — while the real card rested in my wallet, thousands of miles away.
I was issued a new card, of course, and the old one voided. The new card is still not chip and pin, despite me explicitly asking for it.
I'd love to take on the "hassle" of public-key crypto.
[1] This was a debit card that works as either a credit card or a debit card (though the latter mode requires a pin, but the former mode requires nothing … because … waves hand); I am told credit cards are supposedly less of a pain.