I've always been asked for a serial number when redeeming, so I just presumed it was to prevent you from re-using it when you fail to present it at check-in.
Interesting.
I have never been asked for a serial number when I called.
They asked just for "Star File" number, though.
My last call was last summer, so it was a while ago. Maybe things have changed since then?
Last three times I didn't even submit the paper certs at the airports which happened last fall and last month.
I don't really know what to do with the (un)used certs...