Art is not writing, true. Distinct symbols and syntax are required for writing. But it need not be transcription of anything spoken.

Yes writing systems evolved from earlier symbols used to indicate general concepts without a linguistic context. And those symbols go far back into the ice age -- we see such symbols on the walls of cave paintings in Europe, for example. In the case of Sumer, we certainly know that the writing system derived from accounting symbols for livestock and grain and such.

But going from simple context-free symbols to transcribing spoken language or thought with grammar and structure is a conceptual leap worth tracking.