I'm With Bobby:
My Maytag centre-dial dryer came with a heavy coat of softener-sheet varnish all over its drum and door; it took a tremendous amount of work to get things clean again. And while this wasn't necessarily the fault of the dryer sheets, the former owner had run the dryer with a hole in its lint screen - the dryer had blown a couple of softener sheets right through the hole and into the dryer's innards - there was no good reason she didn't have a dryer fire. For good measure, what was left of the lint screen was clogged with dryer sheet residue.
Feh, sez I.