Oh, and by the way: Just because someone is constitutionally elgible doesn’t mean the american people would or should elect him or her.
We have Communists, Mafia bosses, serial murderers, terrorists and doctor-certified lunatics who are all natural born citizens with 2 American citizen parents and 4 American citizen grandparents.
Yes, the founding fathers intended to protect us from some foreign royalty breezing over here and buying his way into the Presidency. But they never intended to “protect” us from every possible poor choice that we could make for President. Specifically, they never intended to “protect” us from electing American-born citizens as our chief executive.
With all the side considerations I believe, perhaps not only my opinion, that the Founders discussed and voted on a very specific terminology of “natural born’ for POTUSA and left the ordinary use of ‘citizen’ for congresspersons and other ordinary citizens you have mentioned. Certainly the people are free to choose among many kinds of citizens that are also ‘natural born’. My belief is that the Founders were wise to use the terminology of ‘natural born’ as a distinguishing feature against any undue foreign influence. I speak as a child of not naturalized immigrant parents, who served overseas in WWII and had an only brother killed on Okinawa. Though not eligible for POTUSA we were willing to give our lives just to be citizens of the USA.