Mastercard and Visa aren't the ones at risk by such activity, the issuing banks are, and as someone who works for a bank, yes, banks have tools to detect and stop account takeovers and assist card members in recovering from such incidents.

Scammers don't care about privacy cards. They'll use anything they can get their hands on, metaphorical or otherwise. If it doesn't have their details attached, it's fair game to them.