I think that there should be some kind of hardware key or smart card system issued by the government, where if you loose it or get it stolen, you can go to the post office or DMV or something to get the old key revoked and a new one reissued. The post office or DMV would verify your identity by biometrics or N other forms of ID.
Everything about you is a data point that could be copied.
Think more of some uncrackable government issued id card, that anybody that wasn't to hack it should go to the police station to get one.
Which you can only do after proving that you are who you say you are - which ultimately involves some (hackable) data.
If only most online authentication was that hard, and with so much risk for those attempting to fake it.
Even if showing up in front of US authorities was completely hackable, it'd still be better than the current state of affairs, because you'd have to hack people one at a time in person. (Unless you discovered some 0day in the key generation process or the hardware or something)
That naturally limits identity theft to a targeted attack on one individual, rather than being able to steal half of US adults identities all at once. Also, the hacker (or their accomplice) would only be able to hack one person per DMV (or Post Office) per month. And they'd have to at least vaguely fit your race, height, gender, etc.
A gang would maybe have the organizational skills to farm it out to a bunch of people. But, that's still limited to something on the order of thousands of people.
Let's not let the perfect be the enemy of the good.
Does it just come down to the cost of copying? Should all businesses who use identity data indemnify their customers against identity theft (as suggested elsewhere in this thread)?