This seems as irrational as the behavior described in the stimulus. Why would playing dead protect small animals from the predators that could make a loud noise or unexpected movement? We still don't know.

If the small animals tried to escape, predators would just kill them. But since predators think the small animals are dead, they store them in a hiding spot, which allows the small animals to escape. This explains the behavior.

How common different predators are doesn't tell us how playing dead could possibly be useful for small animals. Without more information, this is just irrelevant.

Sure, but why is this behavior useful for the small animals which do play dead? This still doesn't explain how the behavior could be beneficial.

Information about animals that don't play dead isn't relevant to us. We need to know why the small animals in question do in fact play dead rather than struggle to get free.