As our fictional character John found out, you are also making it easier for the criminal. You have not secured the systems, tech is still too young, so the criminals can still jump around anonymously. The criminal has a far richer playground now, his marks are open books to him. What is even worse is that when they assume John's identity, John gets the blame and it is then his responsibility to prove it was not him. See the current credit system for how easy that will be.
Lets go back to our initial reasons for wanting anonymity outlawed.
We saw that the annoyance factor didn't change. This is because a lot of what people are annoyed about never violates any laws, it just feels to them like it should. That part of it did not go away with the law. Nor did the civil issues, because the law is a criminal one and the federal government isn't going to support every persons perceived civil case. John still can't afford to sue.