If the Constitution meant Naturalised Citizens couldn’t be President, why did they invent the term “Natural Born Citizen”?
Because they were English-trained lawyers and used English legal terminology. The Constitution is full of phrases that had a technical legal meaning under English law, which was widely understood at the time ("Duties, Imposts and Excises"; "Letters of Marque and Reprisal"; "Bill of Attainder"; "Cases in Law and Equity"; "Corruption of Blood"; etc., etc.-- I could give you 50 examples).
English law recognized only two kinds of subjects-- Natural Born and Naturalized. The Constitution used that terminology.