Actually is illegal
"It does happen to be used as such somtimes, but there is no legal reason to do so"
In fact, the text of the social security act makes it *illegal* to require use of SSN for anything except social security purposes (tax forms count, so an employer can ask for it so they can fill out that W9, since your taxable income is the primary determinant of how much social security money is sucked out of your paycheck.) Companies aren't prohibited from *asking* for the SSN (or more often the last 4 digits) but it's illegal for their to be any consequence of saying "no".
For example, when I worked at the cable co (as a temp), we were to ask for the last 4 digits of the ssn... if they weren't in the system, we'd put them in. If they *were* in the system, this was supposed to make sure the caller was really the caller. (I think for the very few accounts that went to collections*, I think it made it slightly easier for the collection co to ding their credit.) But, if the caller refused to supply them (and they weren't in the system), we were to just put "xxxx" or "----" and add an account note indicating refusal to supply SSN (the purpose of the note was so someone wouldn't think the previous rep was just in a hurry and didn't fill it in). At the customer's option, we could put "see notes" so it'd show on the account screen, and put some other passphrase or password into the notes.
*This was EXTREMELY uncommon, the local cable co works with people pretty well so if they either got a crazy amount of pay-per-view, or lost some income (but had the deluxe cable package) or whatever, pay off the past-due amount over time rather than cutting them off and (when they then don't pay, since they've already had service cut off...) sending them to collections.