The analogy doesn't hold. Not all copyrighted works are or will be culturally significant, but all have the potential to be culturally significant. We have no way of knowing ahead of time. It's regulating haystacks as if any individual straw may actually be a needle.

A work that is not publicly shared has no potential to be culturally significant.

A work that's not publicly shared will not be copied and doesn't need protection against copying to begin with.

A work that isn't publicly shared by the author could be shared by someone else without permission. Copyright law does and should continue to criminalize this.

A work that is not shared has no value and there should be no criminal sanctions to protect something of no value.

You don’t get to misuse violent power of the state to control spread of arbitrary information

Literally everything "of value" that was ever published was unpublished for some period of time.

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.