By which I assume you mean that schools actively teach non-accented pronunciation

From 4 to 11, when I went to boarding school until I was 18, how you pronounced English was, as important to the curriculum as how you wrote it.
If you arrived at boarding school with a trace of a regional accent, your parents were advised to send you for elocution lessons - I felt really sorry for all those guys from Kenya and Rhodesia etc. who had to go to classes when they could usefully be smoking in a hedgrow!
Mrs.Boxer and the Boxette still go into apoplexies when I say: "Have you got a tahl, I want to take a shah"
Yes, I am a man of Kent, Peter, who has lived in Yorkshire since '72, regrettably, you are as likely to hear estuary English in Leeds or Harrogate, as in the SE, these days.