I'm not sure about you. You sure write a lot of words, sort of like a lawyer. (See "words multiplied" in Gulliver's Travels.) But lots of words don't make you right. The Constitution does not give the Court(s) the power to decide anything that Congress hasn't legislated on. You need to reread "and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof." None of this is left to the Court(s) nor should it have been. The only issue for the Court here absent a declaration by Congress is what might be meant by the phrase natural-born citizen.
ML/NJ
Have you read the Third Article? The courts deal with a lot of stuff that Congress hasn’t legislated. They deal with issues between states, with ambassadors, and with private entities where Constitutional issues are at stake, as well as government actions other than legislation. The courts deal with tons of stuff. And they are given the job of deciding controversies that arise out of the Constitution, in both matters of fact and law.
Congress is specifically given the job of deciding on eligibility issues regarding ITS OWN MEMBERS. But nowhere is it specifically given the job of determining eligibility for the President. To do so requires an interpretation of “natural born citizen”, and interpreting the Constituiton is the job of the JUDICIAL BRANCH, not the LEGISLATIVE BRANCH.
The separation of powers matters.