I don't know about the security aspects of the system, but using a driver license number would work for many but not all people. Young people that need catch records and those that need a fishing license at age 15 may not have a driver license. There are also those that just don't drive and don't have a license. In some states your driver license number is the same as your SS #.
I think one reason they chose the SS# is that you must now have SS# for all your kids to file your income tax so it is a unique number that most people already have.