Or you could say it would take just a few generations be born before they would qualify. The way I wrote it, you as a naturalized citizen may not qualify, but offspring of your son or daughter would, provided they wed another citizen. The problem would correct itself quickly. And today there are natural-born in plentiful numbers.
I have read what was said in various founders documents, and the intent was to preserve the heritage of America by the natural-born requirement — why else would they do it?
All four of my grandparents were U.S. citizens, as are my parents; but by your made up definition I would not be a natural born citizen, as neither of my parents would be, because neither of my grandparents would be, because all four of my grandparents had at least one parent who immigrated from Europe.
Almost every American has at least one immigrant within their parentage if you go back four or five generations. According the definition that you made up, none of them would be natural born citizens.
And the problem would only get worse, as the few who would fit your made up definition would no doubt predominantly choose as a mate an American citizen who had an immigrant grandparent or great-grandparent. After sufficient generations there would be no such thing as a “natural born citizen” according to the definition that you made up.