Just my thoughts...
I'm not real crazy about moving things on the lathe and cloth of any type.
Accidents happen and they do so very fast... I know it's all folded up, however, some people manage to get their fingers in the cloth and the benign lathe becomes a force from hell.
Last year or so there was a video making the rounds of a man who was pulled into the lathe, very horrific.
I personally know a guy who had his "skinned" fingers sewn in his abdomen for a year while new tissue and skin grew. Pained me to see him.
So, I use paper towels and try to ensure my fingers aren't trapped. Do the old pinch grip... Still have had paper towels pulled from my fingers...
If this saves someone terrible pain, then I've done my job of preaching safety. I try to live by the words "Safety First"...