My mother used these until a couple summers ago, and she would swear to you that using them, which can produce a heavy 'thump' in the drum, caused fatigue in a wiring plug/terminal at the motor start switch. This almost led to the scrapping of her 1983 Kenmore dryer.
I was determined to fix the dryer, which wasn't heating, and found a wire plug from the start switch to the heating element to be fatigued and hanging loose, which broke the circuit to the element.
It was fixed after that, but the dryer balls went in the trash. This may have happened anyway and was therefore unrelated, I don't know, but I don't see why that wiring plug/clip would have been fatigued, as it had never been touched prior to it's failure.
G