Congress has expressly stated, in the Nationality Act, that any child born on American soil is a citizen. (In fact, the law goes farther-- any child under 5 years old found on American soil is presumed a citizen until proven otherwise.)
We can debate whether the 14th Amendment requires this or not, but for now, the children of illegals are, at a minimum, citizens by statute.
If Congress ever changes the law, the courts may have a chance to decide the Constitutional issue, but for now, the law is clear.
You are correct and I do understand the law. However, a person should not benefit from an illegal act. It would certainly solve the “anchor baby” problem.
Bringing women into the US from other countries to give birth and then convey citizenship on the baby is BIG business. There is a huge closet industry in New York that caters to Chinese women who pay good money to deliver their children in the US. All in order to gain dual-citizenship.