All my previous experience of using dryers as an adult has been with washer dryers, and I never had this problem before. I don't think my mum's
dryer when I was a kid used to do this either, as there were towels in the house then that had lasted over twenty years.
The towels the dryer has torn are a bit old, but by no means threadbare and they should have had a few more years left in them before they started to look fit only as floorcloths.
The dryer has started to make big holes in the towels and fray the edges when it is on the cupboard dry / cottons settings. Using another setting would presumably leave the towels damp and they would then end up with that cardboard texture, and avoiding that is the only reason to use the dryer. (hardly ever use it for anything else).
Is it a common problem with more powerful tumble dryers?
Any ways to avoid it?