Not for those who value their privacy enough.
Actually, the information you would give the government in order qualify for the prebate pales in comparison to what you give them now when you file your Form 1040. And, the information about your dependents, including their SSNs, is readily available to anyone who digs hard enough.
How does it compare with other welfare programs?
so now we give it easily without need of a cause the government would need. It also belys the fact that the government decides what is or is not a family.
ALL of that personal income information would still have to be reported for Social Security earnings purposes, it would ONLY be eliminated for the income tax purposes.