This isn't a problem in our house. Our DD has tried to hoard in the past, but we've usually managed to clean things up without an overwhelming amount of conflict. Usually the conversation is that we need to get rid of these things to make room for new things, and after a while, she sees our point of view, and even becomes helpful. We've been through this more than once in her playroom, and after she gets rid of the toys she doesn't need, she quite appreciates how she has more room to play.
If this were to be a bigger issue, we'd employ our normal philosophy of "here are some boundaries, within those, go nuts." So in this case, we'd give her a bin that fits in her closet, and tell her that's for all her papers, she can decide which ones go, and which ones stay. And then, as papers start stacking up in random places again, we'd let her know that she needs to deal with those by a certain time/date, anything we find left out after that is going in the trash.
