Concur 100% with John - no point unless your distribution requires it (or you want to sell on Amazon etc) It's also more to do with the record company (recording) side, and not to do with the composer's rights. If you wrote and recorded your own song, that's two separate copyrights to control. Certainly in the UK, there is no need to pay anything to control the rights in a composition and/or recording. We even now have an online court system for intellectual property cases.
As John said, in most jurisdictions, copyright is formed immediately a product is created. All the systems who charge you do is provide a framework to generate reliable and robust evidence that you can use in court in case of a dispute. This is where the often quoted "mail it to yourself" process comes from. This system is nowadays frequently claimed to be old fashioned, out of date and unacceptable, but this is misleading. The purpose of the mail it to yourself system is simply to provide a verifiable piece of evidence. Nowadays, it is even easier to forensically prove that a packaging has not been opened. It will be date stamped by the postal service, with a sign for signature. In any court case, if the content of the packet would support one party, the other party would be able to have the packet inspected professionally to prove the validity of the content - then it would be opened in court and the comparison process started. In many cases, the presence of the unopened envelope serves to discourage continuation of the case. The copyright holder knows what is inside. The other side hopes the evidence simply doesn't exist. Despite many current opinions, nothing has changed with the status of the packet - it is still perfectly valid evidence. Forensics is more solid than ever before, so as an evidence source it's still cheap enough to do. The real arguments come from convincing a non-musical judge that it's the same thing!