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The convention of labeling points in geometric diagrams with uppercase symbols derives (at least also) from Greek mathematics. I cannot judge about the question whether this is the "ultimate" reason. But if we look into Euclid's elements, we find many diagrams where all points and also all lengths (magnitudes) are labeled with Greek uppercase symbols. It is said that Euler introduced the convention to label points of triangles with uppecase Latin letters and sides with lower case Latin letters and angles with lower case Greek letters. Probably the middle- and high-school textbooks, as many other elements of mathematics, adhere to the custom invented by Euler. But when we have a closer look into his books, first of all his INTRODUCTIO IN ANLYSIN INFINITORUM, we find that he used also lower case symbols to label points. So we should drop the word "ultimately" from the original question.