We were thinking of doing a similar approach, basically verifying people's ID upon first purchase. However, we thought it might significantly decrease the number of customers. I suppose there's no free lunch here... verification will sacrifice volume.
In some states in the US, it's illegal to ask for id for a credit card purchase. In all states, the credit card companies don't like it. Here's a good set of google answers about the issue:
This is all to say, credit card processing is incredibly complicated. Here's another quote, directly from the federal government [1]:
"MasterCard wants to hear about merchants who break their rules. Send the name and address and an account of what happened to MasterCard International, c/o Radio City Station, P. O. Box 1288, New York, NY 10101. The merchant's bank will get a stiff letter, ordering it to investigate and bring the offending store into line - or pay a $2,000 fine.
Visa enforces the same rules as MasterCard. "When we hear about a violation, we ask the bank that signed the merchant to get together with the merchant and see that the practice is stopped," Visa representative states. To report a merchant, send a letter to the bank that issued your Visa card.
American Express also prohibits merchants from asking for IDs. "All a merchant is supposed to do is take an imprint, make sure the signature matches and swipe the card through the terminal, to get authorization."