The unavoidable consequence of your own interpretation is that he can't do so while he's in this country. "All persons born" in the U.S., and "subject to the jurisdiction thereof" (according to your understanding of the term) are citizens. Any one to whom these facts apply can't change those facts about him if he's ever on U.S. soil.
Another inevitable consequence of your interpretation is that a person's citizenship can change just from crossing the border back-and-forth. He's in the country, he's a citizen, he leaves the county, he's not a citizen.
Yet another is that a diplomat's child who's born here, and who later comes back on a non-diplomatic passport, can be considered a U.S. citizen. After all, at that point he's liable to the ordinary judicial process for violations of our laws, and therefore "subject to" our jurisdiction, according to your use of the phrase.
So, how many absurdities are you willing to look at before allowing just a smidgen of common sense to govern how you read this thing?
There is nothing that prevents you from renouncing your U.S. citizenship. What I'm saying is that you automatically become a U.S. citizen by being born here, but that doesn't prevent you from renouncing it later.
And where are you getting this in the country, leaves the country, business? That's exactly what I'm not saying. And if you mean that slaves formally and legally renounced their former citizenship, show me. Being brought to this country does not automatically make you an American citizen (eg. African-born slaves). Therefore, your children, even if born here, are probably citizens of another country through inheritance. Therefore, using your interpretation of the "subject to the jurisdiction thereof" clause, American-born children are subjects of their parent's country (and consequently, again, using your interpretation (and Carry Okie's) that this was inconsistent with U.S. citizenship), they are NOT subject to the jurisdiction of the United States. The consequence of this interpretation is that American-born former slaves or children of former slaves are NOT AMERICAN. Obviously not what the framers intended.
So what did the framers intend? The first stop is to interpret the plain language of the Amendment so that it makes sense. Therefore, "subject to the jurisdiction thereof" has to mean something independent of whether you are already "a subject of" another jurisdiction. Or you get the silly results above. And the easy result, consistent with the meaning of both "subject to" (see Websters 1928 Dictionary) and "jurisdiction" (see Webster's 1928 Dictionary and the Bouvier Law Dictionary), is that anyone present in this country, is "subject to the jurisdiction thereof" (except those pesky diplomats).
As to the consequence of a diplomat's child born here, and returning here as a private person, that's probably never been litigated, but they might indeed have a colorable claim that they they are U.S. citizens. After all, the amendment doesn't explicitly say that "born" and "subject to" have to be concurrent, and therefore it is a matter of judicial interpretation. I am sure most courts would conclude that they were meant to be concurrent. And it seems to me that most methods of interpretation would lead to the same conclusion -- textualist, originalists, living document etc.
What the Amendment is NOT silent on, is who it refers to (persons in general, not just slaves), where they were born (in the United States), and whether or not they are immune from U.S. jurisdiction. And since no one here other than diplomats and their families are immune from U.S. jurisdiction, voila! If you are born on U.S. soil and you're not a diplomat's child, you're a citizen.
And despite what you might think, I am not paid to do this, and much as I've enjoyed this tremendously, I really really have to get back to work...