"Well, I think the burden of proof is on you to show why language mistakes matter at all."
Most importantly, because they inhibit efficient communication among parties. The lesser problem is that they might signal low educational status and/or incompetence: I know there is no such thing as "standard English," but you can get pretty close to it through guides like Diana Hacker's _Rules for Writers_. The further you get from this thing that's close to standard English, the more likely you are to sound incompetent or incomprehensible.
If someone comes into a job interview -- or YC interview -- speaking AAVE, or some wildly non-standard form of English, they're probably signaling that they haven't figured out how to speak, if not "proper" English, then a form of English that will allow them to communicate with high-level technical workers. They're not likely to get the job or the funding or the lawsuit won or whatever it is that they're trying to accomplish. _That's_ the problem.
There isn't a central authority because there doesn't need to be: as Foucault might argue, there are merely different loci of power or force that tend to create webs of what is acceptable or not in a given situation.
"The fact is, language changes over time like any other fashion. If you don't like a particular grammar or a particular fashion that is a matter of taste."
Which is all very interesting until you're applying for a job or writing a research paper and you can't write something very close to standard English, at which point you're not going to be able to achieve what you want to.
"You can make the argument that using Standard English (and wearing a suit) are useful social conventions to adopt when going to a job interview, but I think the usefulness of either judgment ends there."
I don't. The fundamental issue is what you signal and how efficiently you communicate. Whether you wear a suit or not has little to do with how you communicate verbally or in writing; whether you can speak something akin to standard English matters enormously.