Now later on eventually yes you could finally go and get parts anywhere and that occurred. My guess is info finally got shared but back then no one had it but Sears. It was that and stores could not cross reference. Believe me we tried.
One store in our city had every appliance part made except Sears products. It always ended up in a trip to the nearest Sears warehouse/parts center and eternal backorder.
You could always get the part you just needed the proper cross reference. I have no doubt that sears didn’t make it easy to find them but given I’ve had kenmore in my home my entire life as well as craftsman I can tell you that the folks who repaired thing as a profession have always known how to cross reference the original manufacturer.