Citing repealed legislation just adds to the level of your ignorance in the subject matter at hand. You underlined "the children" as if that means all children, Well let me help you out by using the Supreme Court & the Justice who wrote the WKA decision:
OK, now that we have traced the history and found out that nothing had changed regarding children born to aliens on US soil since the time of the adoption of the US Constitution to the ratification of the 14th, we can now return to the 14th. Using the precedent set forth in all previous legislation pertaining to US citizenship and the legal document that gave it its force that was cited & upheld by the Supreme Court in both the Minor & Elk cases, let's see what the paths to US citizenship are? Are there really only 2? YES!
All persons ... Chief Justice Waite in 1874:
The words all children are certainly as comprehensive, when used in this connection, as all persons,
born or naturalized, and subject to the jurisdiction thereof ... again Chief Justice Waite in 1874:
Additions might always be made to the citizenship of the United States in two ways: first, by birth, and second, by naturalization and that Congress shall have power to establish a uniform rule of naturalization. Then 10 yrs later Gray upholds the ruling of the court written by Chief Justice Waite as it pertains to the paths to Us citizenship as it stands under the 14th Amendment:
The distinction between citizenship by birth and citizenship by naturalization is clearly marked in the provisions of the Constitution, by which
No person, except a natural born citizen or a citizen of the United States at the time of the adoption of this Constitution shall be eligible to the office of President, and The Congress shall have power to establish an uniform rule of naturalization. Constitution, Article II, Section 1; Article I, Section 8. By the Thirteenth Amendment of the Constitution, slavery was prohibited. The main object of the opening sentence of the Fourteenth Amendment was to settle the question, upon which there had been a difference of opinion throughout the country and in this Court, as to the citizenship of free negroes ( 60 U. S. 73; Strauder v. West Virginia,@ 100 U. S. 303, 100 U. S. 306.)
This section contemplates two sources of citizenship, and two sources only: birth and naturalization. The persons declared to be citizens are all persons born or naturalized in the United States, and subject to the jurisdiction thereof.; The evident meaning of these last words is not merely subject in some respect or degree to the jurisdiction of the United States, but completely subject to their political jurisdiction and owing them direct and immediate allegiance. And the words relate to the time of birth in the one case, as they do to the time of naturalization in the other. Persons not thus subject to the jurisdiction of the United States at the time of birth cannot become so afterwards except by being naturalized