I suppose what I'm really asking here is this:
When you ask someone to enter their credit card number on a checkout page, that number is so glaringly obvious that it doesn't necessitate explanation. Everyone seems to know that it is the 16-digit number on the front of your card. You don't need to explain to people via text and diagrams that it is such.
So why isn't the CVV also self-explanatory? How could we make it so? If things like the card number or expiration date don't require documentation, why are cards not designed to make the CVV easily understandable?