I agree with your sentiment, but I have to point out that our government doesn't want to find the illegals (or stop their infiltration), but they do very much want to document and locate privately owned firearms...and we both know that they intend to remove them from private hands. Their strategy is and will continue to be incrementalism. One sensible law at a time. We must never kid ourselves about their ultimate goal, or their willingness to use whatever means to accomplish it.
I know they would like to know where all the guns are, that’s what the “universal background check” ruse is all about. Outlawing private sales. Documenting every transfer.
Once they know where they are, they can go get them.
I’m doing my part to make sure they are frustrated.