Aside from the other replies you've gotten, it has long been a standard in the courts that you can not benefit from illegal actions. Strangely, the same issue with illegal aliens getting anchor babies is the same issue with burglars successfully suing homeowners for injuries that occurred during their crimes. Both should have been laughed out of court when first brought up. It will be interesting to see if any tort reform appears on Trump's agenda as well. Clear up some of that junk as well, and you'll effectively double the number of courts in the nation as the caseload is slashed due to the elimination of the lawsuit lottery or extortion suits.
I am told that the Immigration and Nationality Act of 1965 and additions thereto have been the foundation for Anchor Babies.... that seems correct since the subject never came up before that... I have been around a long time.
I can’t find the particular portion of the Act that is pertinent but believe those who insist it is the Fourteenth Amendment that permits it are throwing up smoke screens.
The ACT can be repealed... easily if public opinion is strong enough and someone brings the issue into visibilty as fixable.