Everybody thinks that RPN is about the inverted order when it's really about having an explicit stack instead of an implicit one.

If you're using "algebraic", you sometimes have to put a "(" into your expression a long way ahead of when you need it. Think of how many times you have to go and fix up your left parens when writing C code conditionals. On a calculator, if you screw up, go back to start. Also, old calculators had parentheses limits.

"Modern" algebraic calculators mitigate this somewhat because they can enter the expression in text form on a dot matrix LCD so you can go back and add/delete parentheses as required.

An explicit stack means that I can start and stop subexpression calculations at various points and cache the results. It also means that I can rearrange precedence at my convenience--of course, the flip side is that precedence is my problem instead of the calculator's.

With RPN you can just type facts in as you think of them, and figure out how to combine them later. With conventional entry, you have to have the entire equation in mind from the beginning, or backtrack to add brackets.

RPN has no use for brackets, because there is never any ambiguity.