> It is

It is not, as explained by your own link. You should read your own link. Registering makes it enormously easier and nearly everyone will register prior to bringing a suit, but it is absolutely not required -- again, as your link clearly explains.

Furthermore, your point is academic because what people do in practice is simply register just prior to bringing a suit (after the infringement takes place)

> Service providers don't take things down in the absence of any proof of a copyright.

Yes they do - in fact the DMCA requires them to do so.

> You have unlimited time to register. It's not 5 years. You just need to register prior to bringing a suit.

The 5 years matters, but yes, this is why your point about registering is entirely without merit.