I'm not sure the concern with bigs and littles has to do with hazing.
My chapter also did sister-mother/sister-daughter during the new member ceremony. Sometimes you got wonderful mom/daughter match-ups, and sometimes you didn't. I never knew any other way. I was taught that a sister-mother was AGD's formal terminology for a big sister.
I was astounded when I met Junior Circle members from other chapters who were doing rose sisters, big sisters, and what-have-you. I think the reason there is a push for sister-mothers/sister-daughters is because there should be uniformity among all the chapters. Sister-mothers are what the Ritual calls for, so that is what IHQ expects us to follow.
I'm not really sure what else to say.
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