>There are hundreds of thousands of people who come into the country every year through other visas (and also on H1B from other countries) and naturalize and take up jobs in the country. But that doesn’t matter because they are now US citizens.

What you seem to be saying is that the problem is worse than we think for natives because of these immigrants dropping off of stats after they become citizens. Of course I think this myself. It doesn't matter if you make these people citizens so much, the point is that their effect on the job market is independent of citizenship.