I think it is important to teach children to argue their point, and to do that, they need to see beyond the way their 'opponents' present themselves, to what is actually being said. That means getting past irrelevances such as accent, or minor differences of grammar, and looking at the actual argument.
It can be difficult to do that if you get used to people who 'talk nicely' being deferred to, and those who speak using dialect or non-standard forms of English being pilloried (and yes, Angela Rayner is a great example of this).
In my work I often heard students from public school backgrounds getting respect (from other students) for arguments that were full of holes, and those from comprehensives having to try much harder to get their ideas heard. It is silly to pretend that this doesn't happen way beyond the education sector. Excrementum vincit cerebellum, as the Romans never said
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It's not all about accent - it is about confidence, poise and a learned ability to put your point across. People used to go to university simply to learn rhetoric. That is where the later idea of 'grammar schools' came from, too. It is taught in public school, and Starmer wants to extend that into the state sector. If this initiative gets people over that hurdle I think it will be a good thing.