When I first started the indie publishing process, I wanted to do it correctly. I scanned a few "How to Indie Publish" books and found them all lacking. Most had titles like, "How to Publish in 17 Minutes". Amazon was the worst noting you can publish in just 5 minutes. Copyright setup took about 2 hours. Submission about 25 minutes. Confirmation and payment, 10 minutes. Waiting for this to come through took 9.5 months.
For any author, copyright protection is worth pursuing. While Amazon is correct and you can publish within just 5 minutes, that presumes you've DONE EVERYTHING ELSE that takes much longer than 5 minutes. In my own journey, I learned that there is a TON of content about how artist-created content has an inherent copyright. The issue becomes should you ever want to enforce it. I don't want to enforce ever, but having invested so much time in it all, I wanted to have the copyright protections.
Digging around, it seems that less than a 3rd of indie content has copyright protection in place. That's a bit scary if you think about it. Imagine spending all this time creating an awesome story and then one day, you stumble across a differently-titled but same content story by a different author. Without registering protection, actually proving to Amazon, GoodRead, or whoever will be impossible. It will wait for a civil lawsuit you'd have to file first. Now, go even more worst case... the cheating-author files a lawsuit against you. It's your work. Register and protect it.