The Common law requires perpetual allegiance to the King. Our very existence is a renunciation of English common law. If we had adhered to it, we would not be an independent nation.
But of course, you will argue that we rejected THAT part, but we KEPT the other part. Sure we did.
Of course we did.
We threw out what we didn't want, and kept what we did.
We didn't go and adopt the French language just because we gained independence from England.
We didn't go and rewrite the entire legal system, either. In fact, every single state either adopted the English common law in general, except for the changes they legislated, or adopted the same rule for citizenship as the common law.
Heck, one or two of our States didn't even adopt a Constitution at first, but continued to operate for DECADES under their original ENGLISH charter.
So your claim that we must necessarily have come up with some new way of determining citizenship (though you never can produce any actual evidence whatsoever that we did) is beyond idiotic.