^^^I think that's a really interesting question. And while I don't KNOW the answer, my guess is the process started just because that's what private clubs do. Junior League to Exchange Club all require recommendations, regardless of how seriously an individual club will take that process.
But considering the NPC sororities don't seem to have fought too hard against the race issue (we did adapt relatively early in the civil rights movement, if not exactly warmly or across the board), I would guess it wasn't with malice, just an unknowing sense of entitlement. Many women throughout the last 50 years (and still) don't get that the process alone of requiring a rushee to get recs can be racist or classist (and yes, I agree that it is more classist than racist).
I would love for this to be the reason that all sororities eliminate the requirement for them. But we know how much my opinion is worth.