Luckily we rely on the text of the amendment, not on the comments of some legislator, in this case Sen. Howard (of Michigan, BTW), author of the Citizenship Clause. There was extensive debate at the time about the meaning of the amendment and Senator Turnbull and President Johnson, among others, weighed in on the side saying that it meant children of aliens would become citizens.
Like it or not the reality is we interpret amendments based upon what they say, and the Supreme Court is the venue we use to resolve disputes. So despite what Sen. Howard wanted the amendment to mean it actually means what the courts have consistently ruled for well over a century.
Actually, no court has ever ruled in favor of "birthright citizenship" as it applies to an illegal alien.
It is thought that the State Department somehow started the trend.
Wong Kim Ark, recall, did not apply to illegal aliens. The parents were clearly U.S. citizens.
I don't think it's quite that simple. I don't mean the Constitution is difficult to read and understand, obviously, but I would argue that context and the drafters' choice of language as understood at that time is relevant to interpretation.