You have to go back to what the founders meant by "Natural Born Citizen."

It meant being born (a) on American soil (b) to two American citizen parents.

Remember, there was no such thing as a general US citizenship. Everyone was a citizen of the State where they were born, and therefor could be referred to as US citizen (until the 14th screwed it all up).

The only exception was for those who were living at the time of the adoption of the Constitution, because the USA and citizenship of the States did not exist until the British colonies broke away.

Why would they want ONLY a natural born citizen -- and not just any citizen?

Because of loyalty. Loyal to America, not the foreign country where they were born.

This is also why the 14th Amendment includes "and subject to the jurisdiction thereof." Any child whose parents were citizens of another country are subject to that foreign country.

Two Mexican citizens invade the USA and have a baby. That child is subject to the jurisdiction of Mexico, and therefore are Mexican citizens.

The idea of the anchor baby is not law. It is merely a regulation on how to interpret the law, and that can be reversed with an executive order by the POTUS.