I suppose I should change the title to say “Why an AsciiMath Dialog” and then add another subsection “Why not AsciiMath”.
The short answer is that AsciiMath is an excellent language IMO but a rather lacking implementation. Shortcomings of this particular dialog are raised in a different thread here, but for me personally the biggest issue was in the output format. AsciiMath is pretty tightly integrated into each implementation (like MathJax) instead of just outputting standard MathML. I also altered the dialog a bit, e.g. the matrix notation is a bit different in mathup, and I also add the possibility to use whitespace to group sub-expressions (similar to typist).
There are also small differences in the language, main one being the use of whitespace to group expressions in mathup (similar [but not identical] to typist).