Chris,
I was pleased when I started reading your note, distinguishing between authenticators and identifiers, because I thought you'd see the point of this distinction. But no :-( The original poster is 100% right. Society needs a good _identifier_, because the main alternative "name + address" is messy and too fluid. But there should be no secrets to this. The best way of driving home that SSN is an identify - like "name + address", but better - is to make them all public. But there's one more step.
If I go into your bank and give them your name, and your address, and they let me empty your account, no one would dispute they were foolish and legally liable. But with identity theft, we are constantly blaming the entities the let info (like SSN's) slip yet I scarcely ever see criticism of the real culprits. This one is easy. SSN's were not designed to be secret, are NOT secret, and are easily guessible, and if someone (a bank, a business, whatever) treats them as some secret password (an authenticator) - which they were never supposed to be - then they should be immediately 100% liable for all damages including consequential damages. Yes, it would be harder to open a new account, etc, but the price would be worth it because the people who _should_ be guarding against identity theft would finally have incentive to do so (wherease now they have none.)
Use SSN to "prove" identity should be treated the same as citing a name and address to "prove" identity. I.e. obviously unfair, idiotic, and culpable.
Identifiers are not authenticators. We need to a good identifier, and SSN's will do fairly well in the U.S. Let them be that! Don't hide them. Anyone who thinks that since it's a good identifier, it must be a good authenticaor, has no business running a business like a bank.