I just wanted to say that there is a sportsbook out there (http://www.pinnaclesports.com), and they do exactly what was stated above. They say in the welcome email that they will need verifications of the credit cards used when depositing. Everybody has to do this, after they deposit.
I think that this is a good way to prevent abuse of credit cards, and big players would feel more comfortable because they know that all the verification is taken care of and that there is no reason anymore for them not to get paid quickly.