I disagree that grammar is a free-for-all,
I didn't say that grammar is a "free-for-all", I referred to "general use" which is what descriptive linguists use as a benchmark for determining the norms of the language.
and that the rules for written English should change arbitrarily based on the way words are spoken.
Why not? Surely it is better to determine the rules according to how they are used rather than to base the rules on how they are arbitrarily chosen by prescriptivists.
Written and spoken language are already quite different, and the same rules apply to both.
In fact, even within spoken and written language there are differences depending upon the context. I would think that "Back in 5 mins" is no worse, and probably better than, "I shall return in five minutes." if it was written on an informal note. There are also different norms in fiction, news, academic papers, Twitter, comic books, cover letters to potential employees, and internet forums (fora?). But language norms change according to time and region, and in many ways these language changes are not predictable. By that token you can indeed argue that words change arbitrarily according to how they are spoken.
This is why when you listen to someone on a podcast, you can almost always tell when they're reading from a preprepared script.
This is something that you can almost always tell for a number of reasons. People also often slow down if they are reading words aloud from a piece of paper.
It is easier to read good grammar than it is to try and interpret bad grammar.
I suppose that depends upon your definition of "bad grammar". A prescriptivist may get angry at "bored of" and insist it must be "bored with", or they may insist that the third person singular cannot be "they", yet they may also then use it themselves and often nobody notices.
Most of us read good grammar without having to think about it.
Why should reading without thinking be the goal?
Relax the rules of grammar, and reading comprehension slows down.
I think plenty of reading comprehension is possible without having to use "good grammar". After all, we have no difficulty reading and comprehending "Me and Julio Down by the Schoolyard" and not only does Paul Simon put himself first and use the object first person pronoun, he also fails to use a verb!
Of course, it depends greatly on your target audience.
Yes, and the context. Remember that the OP was watching a TV show in which someone in the show said, "Cody and I". I very much doubt this slowed very many people's comprehension.