I can see why people didn't want them.
I too would rather not have a stiff blade like plastic meterial nearly cut my head off everytime the car breaks.
By comparison today we have luxurious silk strands that don't pinch anywhere.
I have to wonder how much of this is due to ~fifty years of aging of the belt material. It's not as if the very first time we'd ever designed and installed an operator-safety belt was in the 1970s... so it'd be very surprising if the designers chose to make them stiff blades. Your description is also at odds with how I've seen people handle and use seatbelts in motion pictures from the era... from what I've seen, those belts look to me to be reasonably flexible.