I am not talking about mail yourself a copy. This is not meant for digital stuff anyways and there seems to be no evidence that this is more than a myth.
The US law system is broken anyways in more than one way (like separation of powers), but needing that registration for anything is breaking it even more and that you do need it for anything might even be unlawful since 1989.
And I did not say, you receive copyright. This might be a translation issue. English is not my native language and not even the copyright concept is easily understandable.
You have the copyright by being the creator of a work. As a concept it basically says that you are the creator and this is the primary, the secondary is just some consequences of certain laws that assert that certain things can only be done by the creator or with permission of the creator. There are remnants of this still seen that the copyright ceases in relation to the death of the work's creator - and not in relation to the work's creation date.
It loses all meaning linguistically, if you spell it out: the right to copy. A what now? A right as in human rights? The right to vote? And for what, copying? What about copyrighting physical objects? We have no StarTrek replicators. Those terms were coined before digital copy was available. And like coining it was meant, as in minting. About after the book press was invented. There was no copy right with handwritten books, and those were copied a lot. I think it got an overhaul when music recordings became possible.
But enough philosophicals. Trivially, if you do not publish your stuff, how could anyone violate your copyright. So publishing the item will make it public and therefore documented with you being the creator of the work and the time.
Sorry for ranting and babbling. This whole topic is too complicated and the protection granted by laws should not be dependent on the money of either party. It violates my sense of morals.