Is it only used by businesses? Don't you have to provide the SSN for your driver's license? If the government is using it as an ID across it's departments, then it is an ID.

Those are two separate statements. 1. It's an ID number in the Social Security System.

2. It's also now used as an authentication mechanism by many businesses (because it's relatively ubiquitous and banks, gov, etc. assumed that the SSN owner would and could keep it secret) :

    a. accepting card payments on stripe (https://support.stripe.com/questions/why-do-you-need-my-date-of-birth-and-4-digits-of-my-social-security-number)

    b. driving with lyft (https://www.lyft.com/drive-with-lyft under "What are Lyft’s requirements?")

    c. also for bonus points take a look at what happens when you search google for "SSN for resetting" and marvel at all the banks that let you reset your password with your SSN.

(update to try to fix formatting)