Even the US gov't gave up on the notion the SSN was not to be used as an identifier. My dad's SS card had a phrase printed on it saying so. My SS card did not have that text.
My SS card has that text. I got into an argument at the DMV when they asked for it. I relented because I needed my drivers license.
Congress could solve this by enacting a simple law. Something to the effect of SSNs shall not be used as a means of identification by any party, governmental or otherwise other than the Social Security Administration. Use of an SSN as identification shall be subject to a $100 fine per each SSN used as identification, per day.
