The Founders wanted the President to be a NBC to ensure that the ONE person sitting at the top of the Executive branch has UNQUESTIONABLE, UNWAVERING loyalty to the United States, first and foremost.
At one point, the delegates writing the Constitution in 1787 considered THREE "presidents" in the Executive for "checks and balances." They considered a NBC clause for Senators as well. Debating those issues, they felt that a NBC clause for Senators would limit the pool of possible candidates and could cause bad feelings with immigrants needed to "jump start" the newly-formed republic.
In the end, the Framers compromised that Senators be required to be US residents for 9 years, while striking the NBC clause for the office.
The Framers also compromised on ONE Executive vs THREE. But to ensure "checks and balances," the Framers inserted in Art II, Sect. 1, Clause 5: "No person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President..."
The NBC clause was NOT an accident, nor was it an inane rule to be restrictive to immigrants, and it certainly isn't just a "political" issue ... LOYALTY to the US is the reason the NBC clause was inserted into the Constitution for the POTUS.
Remember this from Fight The Smears?:
As a Kenyan native, Barack Obama Sr. was a British subject whose citizenship status was governed by The British Nationality Act of 1948. That same act governed the status of Obama Sr.s children. Since Sen. Obama has neither renounced his U.S. citizenship nor sworn an oath of allegiance to Kenya, his Kenyan citizenship automatically expired on Aug. 4, 1982.
LOYALTY is at the HEART of the Natural Born Citizen clause for the President of the United States, and that's a BIG concern with Obama sitting in the chair.
Because let me tell you, they're not.
For the record, nothing in your post refutes the proposition that all persons born in the United States, and subject to US jurisdiction at birth, are natural born citizens.
Furthermore, nothing in the Constitution, or in the writings of the founders, indicates that having dual citizenship at birth negates the natural born status of a child born on US soil under US jurisdiction.