Visa is probably easier to deal with in the case of fraud than what it sounds like privacy.com is like.
I use a single CC for everything (that I'm willing to pay with a CC for.) It's been compromised to the point that charges went through 2-3 times over the past decade and a half. CC company caught the fraud each time, automatically charged-back each of the fraudulent transactions, and overnighted me a new card. They also moved all of my recurring charges to my new card (somehow.) From what I understand, all of the big 4 CC companies operate more or less the same in this regard.
This thread has eliminated the chance of me using Privacy.com in the future. If they can't make dealing with fraud at least as easy as a regular CC (which is quite painless, there's no reason to use them.