I think this is a very astute observation, and is arguably one of the most important reasons for learning standard English. One might say that, depending on one’s career and aspirations, having a good grasp of formal English is nearly on par in importance as knowing the rudimentary basics of the language in the first place.
I’ve mentioned before that linguists who defend sloppy colloquialisms and other misuses of the English language invariably do so in impeccable language. As someone pointed out, otherwise they’d have no credibility. If, for instance, you want to defend the use of “ain’t”, you had better do it from a reasoned and learned academic perspective; you won’t get anywhere claiming that “there ain’t nuthin’ wrong with sayin’ ‘ain’t’”.
Those who dismiss the value of promoting strong skills in writing and speaking by deeming it “classicist”, and the domain of “elites” and the “ruling classes”, would do well to remember the importance of speaking to your target audience in their language, in their own linguistic register. And if you want to get anything consequential done in this world, this is precisely the group that you may often have to appeal to.