> First off, immigrants tend to have more children

First, undocumented migrants intercepted at the border by CBP (which is what your source counts) are particularly unlikely to have more children in the United States. Second, the CBP report your source is based on counts encounters, not people, and notes “The large number of expulsions during the pandemic has contributed to a higher-than-usual number of migrants making multiple border crossing attempts, which means that total encounters somewhat overstate the number of unique individuals arriving at the border.”

You're neglecting the fact that not everyone gets stopped, people do visa overstays, etc.

We don't know what the true number is and that's part of the problem. If we're letting an unknown number of people in we aren't controlling for housing demand. All we have hard data on are how many are added to the immigration court backlog.

> We don't know what the true number is and that's part of the problem

We have a pretty good idea, but it doesn't mostly come from border encounter tallies like the onrs you've cited.

> If we're letting an unknown number of people in we aren't controlling for housing demand.

Except for a sharp drop during the pandemic and a rebound to nearly the prior level afterwards, the illegally-present population has been basically flat for years, and on a longer term declining since, IIRC, the mid-late 00s.

Source? Immigration courts are more backed up than they ever have been.

Why limit ourselves to only addressing one part of the equation? I say let's ban both immigration AND procreation!