[soundnote]

The writing is still fundamentally Mandarin, is it not? Hanzi just disconnect the writing somewhat from the sound of the individual language, and the languages are closely related enough that you can read written Mandarin reasonably easily as a speaker of other Chinese languages.

At least eg. Hannas - far from an impartial voice on the subject, mind - clearly distinguishes the written standard as a separate language from dialect speakers' native ones:

"By the same token, the 'unity' that Chinese characters allegedly impart to the language by allowing speakers of different 'dialects' to read a common written language turns out to be an illusion. These so-called Chinese dialects have less in common than the Romance languages of Europe, meaning that speakers of nonstandard Chinese (some 30 percent of the Han population) are not reading their own language or even a common language, but what is to them a Mandarin-based second language written in Chinese characters. Granted the characters allow non-Mandarin speak- ers to read segments of written Mandarin in their own regional pronuncia- tions. But, far from unifying Chinese, this practice only perpetuates differences that would have been leveled out long ago under the influence of a phonetic script."

— Hannas, Asia's Orthographic Dilemma, Ch.8, Appropriateness to East Asian Languages