This is actually treated as linguistic fact, although we call them "idiolects" when we're talking about that level of granularity.
> not because it is impossible to have prescriptive definitions or grammar, it is just that dictionaries do not even try
They don't try because the field of linguistics has arrived at the conclusion that the role of the linguist is to document what is, not to prescribe what should be. They arrived at that conclusion by studying languages and discovering that they are far, far more messy than prescriptivists had hitherto believed.
The only role that prescriptivism has these days among serious academics is an acknowledgement that while all forms of language are well-structured according to well-defined grammatical rules, cultures assign value judgements to certain forms of speech and so it's valuable to learn your culture's value judgements and learn to speak and write in a way that earns you credibility in your culture.
But even this looks very different than the prescriptivism of old, because what forms of speech and writing get creds vary dramatically from generation to generation, place to place, and even context to context. Learning the grammatical rules taught in traditional schools will not help you fit in on modern social media.