I'm not sure I follow your claim that "all writing systems...are systems for writing out speech." I agree that "most written characters are based on the SOUND of spoken morphemes" but this isn't by itself proof of how written language is processed by the brain. Certainly ideographic cuneiform counts as writing just as much as modern english. As writing grew more complex we can see a shift in every culture that started out with ideographic representation to move to a system much more dependent on morphemes. But in every case, the shift is gradual and subsumes elements of the purely ideographic writing, proving that the early ideographic writing was seen as just as much a language as the newer script that includes phonetic elements. We do after all, use a language defined by phonetic features.
Do you have pointers to discussion of purely-ideographic language writing with no phonetic component?