Vanishingly little copyrighted material is culturally relevant. It seems silly to paint all copyrighted material with that brush.
You don’t get to misuse violent power of the state to control spread of arbitrary information
Also, people may keep works private not because they lack value, but for other reasons.
As a very simple example, a someone might take a racy photo for their own private use, not because it would have no commercial value, but because they prefer not to commercialize it. And there are hundreds of other reasons why someone might choose not to share a work with the world.
As much as I wish that my meeting notes from my standup this morning were good enough to become a cultural icon, I'm pretty sure the entire planet, including me, will forget about them next week. Mundane creations like this consist the vast majority of copyrighted works.