Why are there "exceptions" at all? You mention Ambassadors, but you leave out two other important "exceptions." Slaves were not citizens either. (Unless they had first been manumitted.) Indians were not citizens (despite the 14th amendment) until 1924.
YOUR theory is FULL of "exceptions." The Jus Sanguinus principle (Which is what ENGLAND ITSELF uses to crown it's head of state) has NO EXCEPTIONS.
Does it not occur to any of you that the existence of "exceptions" demonstrates that it is not a "natural law" principle? Indeed, the "exceptions" for Ambassadors are a result of a "natural law" intrusion into the artificial (man made) principle of "jus soli."
I'm a little surprised that you're holding up England as a model here. Usually when someone quotes the Wong Kim Ark decision to the effect that "The term 'citizen,' as understood in our law, is precisely analogous to the term 'subject' in the common law, and the change of phrase has entirely resulted from the change of government," they get a lecture about how we fought a war and how citizens are nothing like subjects at all etc etc.
But your question illustrates the difference in our approaches to this topic. You start with what you think the law should accomplish--have no exceptions, keep Obama out of the presidency--and poke and prod the actual words in an attempt to make them do that. I try to figure out what the words actually say and mean, even if I don't like some of the results they end up permitting.