There is a very serious question, whether the "Fourteenth Amendment" was ever validly ratified. The Supreme Court has ducked the question, treating it as political not judicial, but it is hardly something sacrosanct.
You are right that it was not proposed until after the War. It was the cornerstone of the punish the South campaign, launched by those led by the despicable Thaddeus Stevens, and motivated by a combination of hate and an ideology that Karl Marx found appealing.
But as I said, the implication is in the original Constitution, without the amendments, that a person born in the US is a US citizen. It's in the qualifications for President section of Article II.
Besides that, just because the 14th amendment has been misued, doesn't mean that it wasn't a good idea in the first place. It's really just an expansion on the original document's guarntee of a "republican form of government" to the states. (Art IV Section 4). At least section 1 of the amendment, which are what has been misued by the courts. They'd have found a way to do what they wanted to do, even absent the 14th amendment.