When I used to teach mature students, I noticed that those who were smart enough to adopt an 'academic' way of writing undoubtedly increased their chances of doing well on courses and in exams, but in the process they lost something, in that their writing lost a liveliness and sense of who they were and where they had come from.
Yes, I think it's important that children learn to speak and write grammatically, otherwise they risk being disenfranchised - posh, rich people make sure their kids know how to do these things. Fortunately, the development of language is somehow greater than these petty, get on in the world concerns. Through years of teaching and listening to my students, my own vocabulary has been increased enormously - when I can't be bothered to do something, I always now say 'I can't be arsed' - it has a wonderful, deadpan English ring to it.
On a slight digression, as someone who has hearing difficulties, what I really appreciate is not people who speak in a posh accent, but those who really enunciate their words. Now you're cooking with gas!