What strange choices. For example, to express the sum from i=1 to n:

    sum_(i=1)^n

How about using some symmetry instead, e.g.

    sum(i=1)(n)    "Means: sum from i=1 to n"

> Why use the exponent sign to indicate the upper limit?

The caret is used to indicate the upper limit for the same reason some programming languages use it as the exponentiation operator (other programming languages may use something else, like **, neither is normally how exponentiation is “normally”, outside of programming and its historic limitation to ASCII characters, indicated), because its upward-pointing character is a considered a way of suggesting that the following number should be thought of as presented raised from the normal baseline, which is (in somewhat different ways) true of both exponents and upper limits in summation (this is the mirroelr image of why _ is used for the lower limit.)

I think the real answer is "because LaTeX does it that way and everybody inventing their own fancy math syntax used a lot of LaTeX".

That's because the positioning of n is similar to that of exponent? As author says, this is more about expressing "visual rendering" using the text. Hence the term "ASCII math" like in ASCII Art.