The government is the only entity capable of writing and enforcing copywrite protections. Therefore, it is very much the "gubmints" bizness.
If you want copywrite enforcement, the gubmit is the only place to go.
Not necessarily. You own the "copyright" on something the moment you create it (even the US government's copyright office will tell you this on their site). It is easier to enforce your copyright by filing with the gubmint.
What they don't tell you is that by filing your copyright with the US Copyright Office, you agree to a limited exclusive ownership of that work. They will enforce your copyright in exchange for your agreed future relinquishing of those rights.
Patents are for a limited time too. Patents are also publicly visible. There are plenty of products that are not patented (computer designs, the formula to Coca-Cola...) and will never "lapse" into the public domain.
There are ways of still prosecuting those who steal their ideas (enforcing such violations in court can be difficult but not impossible).
As with my earlier example (the Doors), you can get a foreign copyright established on your work and potentially own the work permanently.
It is recommended if you market your works around the world (literary, audio, films, or software) that you copyright them there so that the local authorities can prosecute violations of your copyright. That US Copyright can't be fully enforced in another country.
We are at an interesting juncture because recordings from the 1950s are now lapsing into the public domain in Europe and there are some who say that the DCMA holds no weight in extending their copyright agreements. There has been some talk of prohibiting the importation of such recordings since they are still protected in America.
The "retroactive" removal of works from the public domain (including "It's A Wonderful Life") is a separate disgusting act.