Lower courts are bound by Supreme Court decisions, as you said. And in 115 years since 1898, no subsequent Supreme Court decision has reversed US v Wong Kim Ark.
When a judicial ruling contains errors of fact, that decision is challenged in subsequent appeals.
Whether the decision has been reversed or not is not the point. Nor is it the point that the decision may be challenged in subsequent appeals.
The point is that erroneous judicial dicta is not authoritative and can not be followed. Hence, the discussions mentioned are of no value to a lower court. Lower courts can not rely upon that portion of the discussion.
You seem likewise immune to the obvious paradoxes and nonsensical results which accompany such an interpretation.
An objective person would note, as the court did in Minor v Happersett that:
At common-law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives, or natural-born citizens, as distinguished from aliens or foreigners. Some authorities go further and include as citizens children born within the jurisdiction without reference to the citizenship of their parents. As to this class there have been doubts, but never as to the first.
The court is admitting that there *IS* another view, even though it implies that this is a lesser view. (It happens to be the view you are endlessly championing.)
Your side does not even seem to take seriously the notion that there *IS* another view. How about you spend some of your time looking for and analyzing evidence that the Waite Court was correct in Minor, and that there ARE two different views of the law, and both backed up by various Legal Authorities?
It's called "Objectivity."