The default thinking in linguistics is indeed that spoken language has primacy over written, and Brian has outlined the arguments for it.
But coming from another culture with the burden of diglossia and veneration for old forms of the language, I get where OP is coming from. Written language is never anterior to spoken, and babies listen before they read. But clearly there are cases where primarily written prestige registers do influence what people say. The cases in English are marginal, like pronouncing t in often.
The instances in highly diglossic or culturally conservative languages, like Greek, are not marginal. Modern Greek phonology is a mess, because of a mass of spelling pronunciations, that violate vernacular phonotactics.
Let me give an example. “cheapness” was pronounced [ewtʰɛːnia] in Ancient Greek. If you read it out with modern pronunciation, you get [efθinia]. Now [fθ] is hard to pronounce, and noone probably ever did pronounce it: [pʰtʰ] > *[fθ] regularly goes to [ft] in the vernacular, and itʼs likely that [ewtʰ] just went straight to [ft]. So the modern word for “cheapness” is [ftiɲa].
But because of diglossia, and the primary in prestige of the Ancient written word, Modern Greek got a bunch of Ancient words that were not adjusted for modern phonotactics, and were read out letter for letter. So “responsibility”, which was [ewtʰɛːnɛː], is pronounced as [efθini], not *[ftini]. And it gets worse: “fragile” [ewtʰrawstos] ends up as [efθrafstos]. (Ioannis Psycharis, who was the first populariser of the term “diglossia”, wanted to regularlise Ancient loans like that, as a good neogrammarian. Everyone else thought that regularised Ancient loans were ridiculous—and the resulting unpronouncable phonotactics of [efθrafstos] was not.)
(Of course in reality, noone pronounces it [efθrafstos] in rapid speech; the -fst- at least gets simplified to -st-. When a Cretan dialect retelling of Game Of Thrones went viral, the narrator called Jorah Mormont, whose actor has a Scottish accent, “the Australian tax dodger”, [afstralos]. Because all Commonwealth accents sound alike. YouTube commenters corrected him: a true Cretan would say he was an [astralos].)
Pronunciations like [efθrafstos] came into being because the pedants prioritised the written word. You can say they were fools. You can say languages doesn’t work that way. (God knows Psycharis did.) But Modern Greek phonotactics is now the way it is, because of them.
Ditto the development of Chinese, or for that matter Icelandic.