>"standard English" (that is, "correct" written English) contains rules that are not, and have never been, part of any dialect of English that I am aware of.
It definitely doesn't, mainly because standard English is a dialect of English.
>in standard English you cannot split infinitives
Yes you can, that is not a rule in any form of English and never has been.
>and must use commas (which aren't a "thing" in spoken English) in certain places.
They are a 'thing'. Do you speak entire sentences in a rush without pausing anywhere? No, of course not. Commas represent the pauses that we use in spoken English. People put pauses more or less liberally generally because they use them in spoken English more or less liberally than the norm. If you read a sentence without commas you get lost because you're pronouncing it in your head without pauses. They read as 'breathless'.
>Further, the phonology of standard (written) English is miles away from what anyone says.
Written English doesn't have a phonology, it has spelling. Spoken English doesn't have spelling, only phonology. Lots of people speak General American or Received Pronunciation (rarer, but not uncommon in the upper class) Pakeha New Zealand English or any of the other many Standard accents of the various dialects of English.
You can't pronounce spelling, so of course written English doesn't represent what people say. And there's not really such a thing a 'standard written English'. There's basically American English and British English as spelling, lexical and grammatical systems. Everyone else has their own dialect of speech, but very little if any variation in writing.
>his result of this is that being a native speaker of English is not sufficient for anyone to learn standard English. To do so, one must be exposed to sufficient written material; and exposure to written material tends to correlate with class.
or, y'know, a decade or more of your formative years spending hours at school being required to learn to read, write and spell. I think that should be sufficient exposure to written material for anyone. It has little if anything to do with social or economic class.