Why is Eliza’s lapse into the cockney dialect not only acceptable, but admirable in this setting?

Eliza, who has been warned to limit her conversation to the weather and to people's health, talks about an aunt of hers who supposedly died of influenza but who was perhaps killed so that the killer might steal her new straw hat. Mr. Higgins grows alarmed, and Eliza leaves, but the Eynsford Hills think that by talking about coarse subjects and swearing, Eliza was using a new, fashionable type of slang. Pickering tries to support this assumption by declaring that he can no longer distinguish high society from a ship's forecastle now that people swear so often. Clara declares the "new slang" charming--and to her mother's horror, she herself uses the British curse word "bloody."

In today’s society, do most people think proper grammar and pronunciation is important? Should this change?