Just curious...why don't you mind having a Social Security number?
I'm old enough that my original card still has "NOT TO BE USED FOR IDENTIFICATION" on it. That went by the wayside long ago, and there are few entities you deal with on a business basis that don't have your SS number on file.
And unlike the current use of the chip, having a SS number is not voluntary. I got my number as a young teenager, when I got my first job. Later on, this changed. My children had to have one as newborns before they could even be deducted on my tax forms.
To be blunt, there is little that the chip would do that has not already been common practice for years.