Yes, but it's not up to the copyright holder to decide whether a work is culturally relevant.
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.