I'm thinking shame, not hoarding.
My childhood best friend did this exact thing. She is NOT a hoarder. And she didn't do it forever, just when she was a young adolescent. She put her used tampons or pads (I don't know which she used) in shoeboxes and hid them under the bed. Her mom found them after a while, and told my mom about it. My friend would have no doubt been mortified to know that my mom told me. Sigh.
I didn't do this but honestly I can see the potential for it. I went to boarding school so if I needed pads I had to walk to the store and get them myself, rather than rely on mom buying them. At age 14, I would hang around in the store for a long time, waiting for it to be just empty enough to go and buy the pads. That sounds so stupid to me now, but I was mostly horrified by the idea of a fellow male student happening in while I was buying the stuff. When your period is new, it can be really horrifying. There is so much shame and secrecy about it. Heck, even now it's a little bit embarrassing to tell my husband I'm on the rag.
I would be really surprised if this wasn't somewhat common, like maybe 10% or 20% of girls do this on some level or another when they are young teens. I think the fix is not more shame and horror but just to install a covered trash can in the bathroom so the girl feels she might have more privacy. Or, in really bad cases, maybe give her disposable opaque bags (I'm a tree-hugger so this sort of horrifies me, but I'd still do it to help a girl) and let her "hide" the bags in the kitchen trash or something, if she's really horrified by the idea of her father or brother ever seeing it and knowing what it is.
Oh, I do remember one thing that sort of was nice for me as a young teen. Once my father was getting ready to go to the store and asked my mom what she needed, and my mother looked at me and said "do you need more pads?" I was horrified and blushed and probably said something stupid. My father caught on and assured me that he had NO PROBLEM buying this stuff, he buys it for my mom all the time and this is just more of the same. Then he told me a story that made me smile, that when he was a kid his MOM would make him go buy her supplies, and he admitted to being embarrassed then. But he says with all these years of experience, it's all old hat to him. Well, maybe that wouldn't work for every father-daughter pair, but it did make me smile and relax. I think just the idea that men know "our secret" and it's no big deal to them just made me feel better.