Inspired by the question Is there a "Standard English" - yes or no?, I tried to post directly but was unable, presumably because I exceeded the word limit (I really tried to answer the question simply with a yes or no, but just couldn't).
English speakers can and do oftentimes associate their ideogrammatical tendencies to some standard – usually based on a country. And for that reason only, the term standard English holds meaning for some and therefore does exist.
Conversely, listening to an English language learner (ELL) speak or observing a text written by an ELL, a language educator can make certain assumptions about the standard of English being used. One’s lexicon, pronunciation, form, etc. can be an indicator of this. So from a listener’s standpoint, individuals generalize and thus think in terms of a standard English that is associated with the speaker.
But the question is not if standard English exists (it does), but what variety (or varieties) of English should one teach? Or which variety (or varieties) of English should one accept?
Answering this question will depend on the purpose of teaching an additional language. In a formal educational setting (where exams are administered), the purpose is to yes, learn a language, but more importantly to pass an exam. That is, the variety of English expected in class will align directly with the variety of English included in the exam – imagine if it didn’t! This doesn’t mean the exclusion of different varieties of English in class necessarily, only that the learner recognizes which variety of English to expect on the exam - and most importantly, that the teacher corrects the variety of English that is not considered “correct” on the exam. In formal settings where high-stakes exams are expected, teachers naturally will gravitate towards being prescriptivists more than descriptivists.
Even in informal settings, knowing the reason why an individual is learning an additional language helps direct a language educator in knowing what to correct. Syntax, semantics, and pragmatics pair up with cultural aspects that the language learner is likely to face, and will dictate what varieties of English are “standard” or “nonstandard”; right or wrong, etc.
Other terms like international English have also been used to mean some general acceptance in what varieties of English are (and are not) acceptable. My views have always been not to attempt to claim what is right and wrong from a global linguistic perspective, but to look at what is right and wrong with some local context, particular speech community, situation, location, etc.
So, is there a standard variety of English...no. There is no one standard but many!