The reason you don't want to do that is because they can just reject the postcard. That's why you have to give them needed info on the card. The point of the temp key is so they can get immediate satisfaction.

You could offer other services that having access to a valid key gives you, such as support, updates, community, so on.

That's a pretty good idea, customers might even appreciate the "thank you" note. You do need to get their address though.

Which is an extra layer of fraud protection. :)