It's easier for the credit card companies to just write it off as some fraud and not actually go out and do anything. Realistically most of their early warning systems probably limit their losses to under $1,000 to each card (i.e. the amount of money that someone can charge and get away with before the company discovers the card has been compromised). So figure if even ten people a day get their cards stolen by this method, that's 300 a month, or $300,000 in costs. They probably feel keeping the staff and the equipment to do this costs more than what they'll lose. That and they can always write off their fraud charges on their taxes ad bed debts.
According to a 2002 report Visa's commissions alone were over $455 million. If that entire $300,000/month fee was all on Visa, the 3.6 million a year is a drop in the bucket to them, less than 1% of their commission. Trust me, if it cost them less to setup the system than the money that's lost, it would be done.