Are you really saying that non-ASCII is notation and ASCII is not? When I read your first comment, I understood it to mean that better notation is better than worse notation.
I'm not saying that. Some APL fans say that ASCIIfication of APL is a bastardization, because notation matters. (search through earlier HN threads)
Notation is obviously a shorthand for "sensible notation" or even "better notation" there, because obviously just about anything can be notation. Including laying out pebbles on a beach.
The usual argument is that "one should APL like one reads music", meaning that with experience you immediately recognize specific patterns which help you understand what is going on. As for why ASCII can't do that, only the critics know their true reason, which I suspect amounts to "it's different from what I'm used to". I've done both, and I found J notation no more obscure. Critics should also note that (Dyalog) APL departed from APL2 to copy many J patterns, so it appears difficult to argue that J was such a mistake to begin with.
Some people hold prejudice against parentheses and prefix notation, for others it's ASCII...
ASCII is a much smaller space of possible operators, so an ASCII-based language is always going to end up significantly more verbose than one that allows non-ASCII symbols. I don't use APL but I definitely appreciate being able to write ≤ or ⊆ or ∀ if that's what I mean, rather than having to expand those out in ASCII.
Notation is obviously a shorthand for "sensible notation" or even "better notation" there, because obviously just about anything can be notation. Including laying out pebbles on a beach.
But further than that, I don't know.