Some would argue that the entire requirement is silly, but nevertheless that's where they drew the line.
Congress attempted to address the issue in 1790 with the "naturalization act of 1790", and Vattel addressed it even earlier than that. I personally think that being born in a Foreign country is no bar to serving.
I find no evidence in the writing of the Founding Fathers thought that way as well. Children of ambassadors and military born overseas would have the same standings as children born in the US.
If Vattel is the Authority upon which Article II is based, then the Children born of American Parents in foreign countries in the service of our nation, are indeed "natural born citizens."
If you can show me where in the Constitution it defines Natural Born citizen, then we can hold it above the congressional law.
If you can show me where "Arms" are defined in the Constitution, then we can hold it above congressional law. But if you can't, then congress can ban anything it wants, right? Isn't that your reasoning?
Otherwise, the Constitution set up the powers of Congress to make applicable law.
Which means they can ban any weapon they want to, they can ban any speech (remember, it's not defined in the constitution) they want to, and they can pretty much do anything they want to.
I wouldn't want to live under a government which operated by your theory. You wouldn't either, but you certainly need to ponder how your argument works to their advantage.
You want to add requirements that don't exist in the constitution or in law. As you said before it is axiomatic.