Earlier quoted context omitted.
It's definitely easier to parse programatically, but IMO it's a nightmare to read as a human. e.g. compare these expressions: (x+y)^2 = x^2 + 2xy + y^2 x y + 2 ^ = x 2 ^ 2 x y * * y 2 ^ + + I find it nearly impossible to parse this without actually maintaining the stack in my mind.
It's exactly how you would do the calculation if you ran it by hand, unlike the regular algebraic notation. I am flabbergasted that anyone uses the latter, especially as for most of the history of mathematics calculation was done by hand!
That is probably much more related to why we use prefix/infix/postfix notation: because it maps to our native languages better.