You are conflating citizen with natural born citizen. The reason for the clause in the Constitution was the desire of the Founders that anyone with allegiances other than to this country should not be eligible. Conservatives are like liberals in this. They want strict rules followed but not for their own guy. I think the law actually on the books says there needs to be at least one born citizen parent.
You're forgetting that the SCOTUS recognized natural born citizenship as separate from the two categories of citizenship established under the 14th amendment. NBC is extraconstitutional.
Justice Waite: "The fourteenth amendment did not affect the citizenship of women any more than it did of men. In this particular, therefore, the rights of Mrs. Minor do not depend upon the amendment. She has always been a citizen from her birth, and entitled to all the privileges and immunities of citizenship. The amendment prohibited the State, of which she is a citizen, from abridging any of her privileges and immunities as a citizen of the United States; but it did not confer citizenship on her. That she had before its adoption."
Justice Gray says NBC is OUTSIDE of the Constitution: "In Minor v. Happersett, Chief Justice Waite, when construing, in behalf of the court, the very provision of the Fourteenth Amendment now in question, said: "The Constitution does not, in words, say who shall be natural-born citizens. Resort must be had elsewhere to ascertain that.""
Justice Gray affirms Waite's opinion that Virginia Minor's citizenship was due to jus soli and jus sanguinis, not the 14th amendment, and is, as such, a separate type of citizenship: "Minor v. Happersett (1874), 21 Wall. 162, 166-168. The decision in that case was that a woman born of citizen parents within the United States was a citizen of the United States, ..."