The funny part is, this problem has already been solved by the thru-hiking and backpacking community. We call them "hiker boxes". But for them to work, it requires an agreement within the community on some unspoken rules. Things like take only what you need, try to leave more than you take, and don't abuse the system or everybody loses. Hikers actually enjoy leaving things behind that they hope will solve some immediate need for someone else, even if they never get to meet that person.

Looking out for one another in ways like this is mostly just baked into the subculture and that's one reason hiker boxes work (the other being you just don't want to carry extra weight). As someone who has backpacked through Yellowstone, I'm not sure it would work for the tourist culture there.