Not even remotely. It's defined--for companies, at least--by what works.

Does Phyllis have a strong accent? Let's suppose she does. Hypothetical-Phyllis then fails to have full common-language-privilege. She might not be able to work a phonebank (maybe she has some other privilege that makes that irrelevant)--but when she's the customer she has customer privilege which means that the poor customer service representative has to try to make the best of whatever Hypothetical-Phyllis utters. The representative would have an easier time if Hypothetical-Phyllis learned how to speak in a more mutually comprehensible way, but it's still the representative's job to do the best possible to keep the customer happy (and paying), and if the representative fails too often too badly, and no sufficiently cost-effective remedial measure works (like getting the rep a better headset so they can hear better and their words are transmitted more clearly, if it's over the phone), the company needs to hire someone else instead.

It isn't the privileged who get to define these things--indeed, overly elitist language is going to reduce comprehensibility. The question simply is: can everyone communicate with everyone? If no, maybe things can be improved by trying to use the educational system to move everyone towards mutual easy comprehensibility.

If you can't, well, everything is harder. You just have to deal. For instance, in areas in the United States with a large Hispanic population, it is pretty close to mandatory that every business has at least some people who are bilingual. If your customer only speaks Spanish, and your customer service people don't, you lose their business. It's a problem. Fire that person, hire someone who can do the job. If it's a big phonebank, then para continuar en Espaniol, oprima numero nueve. Otherwise, you have multilingual staff.

People who can speak multiple languages well enough have "multilingual privilege" in this context. And that's entirely sensible. It's too bad for the monolingual speakers who want those jobs, but their skills aren't the skills that are called for. (Ideally, there would be free or low-cost resources in the area to learn the other language--community college maybe.)

You add a bunch of stuff about how different kinds of things are perceived, and those are true to an extent, but none of that was actually experienced in this example.