It certainly seems reasonable that our ancestors would have the need for bedding. A cave floor is far from a comfortable place to sleep without some sort of cushioning and insulation against a hard cold surface. Not that I speak from experience, I hasten to add.
Reuse of the same bedding, over time would render the materials unfit for purpose. As they dry out, so they would become less insulating and uncomfortable and, as Professor Lyn Wadley suggests, the bedding would also become infested.
So, if a group, say 10 individuals, were gathering fresh bedding regularly, might this be an additional reason for our prehistoric ancestors to have been nomadic? After a period of time, and a lot of fresh bedding, even a small group might devastate the near by fauna. This could be an additional factor in the need to move on to where there was ample supply of fresh bedding, rather than travel over long distances to gather their requirements and carry it back to the cave.
Of course there are factors which might make the use of fresh bedding undesirable. Fresh grasses, moss, sedge and other leaves would contain a higher water levels than those which had been used a few times, making the fresh bed damp. Not only more attractive to potential parasites, but also to fungal growth, which could have an effect on the sleepers airway. Also, sleeping on a damp bed is not such a good idea. Perhaps a contributory factor in our ancestor’s short lifespan.
The cold and perhaps damp nature of a cave floor would seem to me to have been quite a draw back to sleeping in caves, but the protection from rain and predators might well have out weighed the draw backs. Having discovered that leaf matter offered some solution to the problems, how long might it have been before raising the bed from the cave floor on a wooden platform supported by legs (a prehistoric 'bedstead') might have become normal practice? And, how long might that 'bedstead' have been used before it, along with the bedding, was destroyed and replaced?