Actually that is not as flawed as you think. Musicians have to register with agencys anyway if they want to profit from uses of their music. In Germany you can't even get a CD pressed if you don't register it with GEMA. (Though that system is a horrible clusterfuck where you have to pay if you want to get money for your music. Basically only very sucessful artists benefit from that, yet still it is more or less enforced.)
I do think it would work for mass market music like that (mostly because I feel most commercial profit from music is heading towards patronage models combined with agency models for long tail profits), and it's easy to implement for traditionally or electronically published books (having a required copyright code alongside or instead of an ISBN works and makes checks easy), but it gets harder on other art forms.
Take paintings or sculptures. Registration would be tricky and checking whether it's still covered would be harder still.
Or photography. If I take a series of snaps and publish them online today they are covered by copyright. I retain ownership and control over them. If I had to register each one, somehow, that's a substantial burden.
Or even just random rambling blog posts and other forms of writing that are covered by copyright today simply because they count as publications and so are automatically covered.
In these two cases I can imagine digital publishing platforms that automatically register materials uploaded, but that has huge potential for both exploitation and unwieldy nature. It's possible such a system could be designed to be manageable. I'm just not sure of it.
And I am generally a fan of that model, I just wanted to attack the idea to see if others can find arguments I've missed.