I am surprised nobody has brought up the most important benefit of registering a copyright.
The largest benefit with the copyright (registered) has to do with litigation and damages.
With a registered copyright you can sue infringers and seek statutory damages and attorney fees. Without a registered copyright you can only go for actual damage and profits which you have to prove.
Registering a copyright also allows you to record your copyright with US customs which helps infringing items to be imported into the USA.
Registering a copyright also gives you a valid and clear ownership record.