At my bank, we try to get as much contact information as possible (including SS# and sometimes even ID info) and explain that if something should happen to the account holder, the more info we have on the POD, the easier it will be for the POD to gain access to the account more quickly.
We don't require a SS# but when it's explained to a customer that the less info we have now, the more the POD will have to provide while already going though a hard time, they generally give us everything we need.