It's worth remembering that the main reason this kind of data breach is a real problem is mostly due to the incompetence of the IRS. For any serious financial organization, knowing a person's SSN, name, address, etc doesn't allow you to access or withdraw that person's finances.
But the stupidity of the IRS means that people are easily targeted by false tax return attacks. File a fake tax return for someone, using their SSN/name/address, but tell the IRS you changed address. Then the IRS sends your tax refund to the new address, and boom, you just collected some poor sod's refund. To add insult to injury, the IRS is probably going to audit the person whose refund you stole.
But the stupidity of the IRS means that people are easily targeted by false tax return attacks. File a fake tax return for someone, using their SSN/name/address, but tell the IRS you changed address. Then the IRS sends your tax refund to the new address, and boom, you just collected some poor sod's refund. To add insult to injury, the IRS is probably going to audit the person whose refund you stole.