Wow. Your experience is radically different from mine. In a normal year, I fly 50-75 flights. I cannot even understand how what you are saying would work. The reader that scans your paper boarding pass also reads you mobile boarding pass. If the gate readers are down, and they are reconciling semi-manually (typing your seat into the computer), they can do that with your mobile boarding pass just as easily. Even fully manual reconciling would work just as well with a mobile boarding pass.
I cannot think of a single time in my last 10 years of travel (probably over 500 flights), where what you describe has happened.
I can assure you that I'm not making it up. I'm 100% sure it was on a layover with Southwest and I'm 80% sure the last time was at the Vegas airport. It was several years ago. Southwest doesn't assign seats, BTW.