Just because you want all the minutia included in a law does not mean you get it. "All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside," is pretty specific, if you ask me. Other law already defines who gets to be a citizen and just being born is not a definition. At least one of your parents has to be a citizen already. I know, my father was one but my mother was not until I was three years old.
Those in this country illegally are not citizens, period. Therefor they cannot pass on a US citizenship. The children born of illegals are illegal themselves and are the problem of their parents, not the taxpayers.
You aren’t listening. That, possibly, is what the law should be. But it’s simply not the law as presently written and/or interpreted.
Your belief that the law is something else has no effect here in the real world.