The hack isn't just SSNs - it includes address history, date of birth, drivers license number - everything reasonably necessary to establish identity. Not sure why the focus is SSNs, any solution needs to be even higher. This is about companies stockpiling our personal information and us having little say in the matter.
The reason the focus is on the SSN is because it enables credit. Privacy is important, but so is protecting your finances.
Recently I called to report a lost credit card, for instance, and the operator read through a list of 10 addresses. I had to confirm which ones I'd lived at at some point in my life, in order to verify my identity.