Registration allows law enforcement to do a better job.
This is entirely disproven by the Canadian attempt to do this.
I provided a link previously, but you can find accounts elsewhere.
The Canadians have a lower population , fewer guns percapata, and a generally good attitude towards their government .
What they found was a low rate of compliance , a much higher than expected expense and a useless list in the final result.
All of these problems would scale up for the US, and if it were done with ten times the efficiency and co-operation of the Canadian experience, the result would still be a list useless to the police for any practical purpose.
Why ignore the Canadian experience? Not that they are the only ones to have the same experience.
I can imagine a circumstance in which a registration list might help solve a crime , but as it turns out this is a pretty rare situation and when the Canadians had their list they didn't use it much.