I believe that cruppers were originally made hard, firm, to prevent soring of the horse. Wrinkles, folds touching the bare underside of tail bone, would easily rub and sore a horse. So it was best to make the crupper of smooth leather, stuffed full of linseed for keeping it smooth, to prevent problems. Yes, the leather still needed cleaning, but horse did better with the full rounded shapes of stuffed cruppers over the long run.
Modern material was not available, nor were the light demands on horses now, part of the thinking in harness makers. Most figured if horse was harnessed, he probably would be wearing harness and crupper for some hours before being unharnessed again. So they used what materials were available, information shared from other harness makers, in construction of harness for working horses.
We have used hard cruppers on horses for long times, not an issue to the horse. Properly fitted in backstrap length, crupper ends being wide enough when shaped in the shop, horse doesn’t get pinches or rubs from hard, smooth material. We do have some modern synthetic harness with plastic type, hard cruppers, which are constructed so they stay wide, no rubbing horses with them either.
I believe that with cleanliness, correct fitting back strap and making sure there is no hair caught under the crupper of the right width, horse doesn’t care if crupper is hard or not in most cases. More of a “people thing” in the person doesn’t think they would like to have hard harness on themselves.
Always are exceptions, so do check the horse for rubs often, clean off the underside of tailbone itself of dirt before harnessing, keep the crupper (leather or synthetic) cleaned after each use with a wipe off of wet rag.