It is part of most financial institution's standard AML and risk management procedures.
It's not a question of advantage/disadvantage, but rather whether Amex and then other financial institutions evaluate your business and then you as worth the AML risk. If not, maybe they revoke the AU, shut down the business card, or other relationships with you and file a SAR.
The lack of the SSN alone isn't going to stop Amex and the credit reporting agencies from matching the AU for future decisions, but it increases the error rate and that's why the SSN is important.
Not sure you're helping yourself or the AU.