I wouldn't say that's necessarily true. I mean in different areas of the US you can pick out dialects from Britain. Plus a lot are mixtures of various accents. Besides the fact there's a lot of other settlers from other nations to throw in to the mix, as well as the natural drift of British accents. There was a study that said a lot of southern American accents are actually close to 17th century British accents than most British accents today are. But who knows how accurate that is.You know, I always wondered how the various British accents turned into the American accents. With Australians and New Zealanders, you can still hear their British origin, but not really with Americans (and Canadians). Odd.
Well, I DO know I've seen some stuff in Shakespeare that just about cracked me up because it could've been said by my great-grandmother from Alabama.
I think it said somewhere (as one example): "I like to have died!" in one play. Which does not mean you WANTED to die, but that you feel like you almost did. I just about blew up laughing when I saw that!!!
Another...you still hear "down yonder" a lot, especially from other people.
Also, doesn't "mad" not mean "angry" in modern-day Britain, whereas it did in Shakespeare--and in America--and other similar examples?
One funny saying I heard about English: "English is a language that lurks in dark alleys, beats up other languages and rifles through their pockets for spare vocabulary"