This is where 3D Secure truly shines; instead of completely refusing a transaction, you can request the issuing bank (= bank of the card used to pay with) to accept the liability in case of fraud (normally, it's the merchant who has to give the money back). Usually the issuing bank will then request the customer for additional challenge, e.g. a 2FA token, a code in SMS, or just their birthday. Some don't even require anything. To you as a merchant, though, that doesn't matter: if the person who bought your product was a fraudster, the money is still yours. Now it's the issuing bank on the hook for fraud, instead of the merchant.
The argument against 3DS is it kills conversion rates (meaning: lots of legitimate customers don't complete that extra challenge, who would otherwise have made the purchase). But for legitimate customers using TOR, I wouldn't be surprised if that number were very different :) I know I wouldn't mind whipping out a 2fa device every time I purchased something over TOR. I mean, fair play, right?
3DS is available today in Europe, Asia and Africa! :'( but not ubiquitously in the USA. Yet. It's getting there.
More info: https://en.wikipedia.org/wiki/3-D_Secure