When I obtain a new credit card, I take care to remember the three-digit CVV number stamped into the back of the card, and then remove the number from the card (very thoroughly, because it's usually stamped very hard into the card).
This is so that you cannot take my card for two minutes and use the printed numbers to do your online shopping. I have, on occasion, had to explain to merchants that they do not need my cvv number when doing (in-person) purchases (these places are usually of less than stellar repute, such as car rental on a Greek island).
I have never had to walk away from a desired purchase because of this practice.
But why, then, is it on the card to begin with, and not provided in a separate "important" envelope in the same way as the PIN? Why is this not a glaring security risk?