Guess it's true in most countries that have been populated long enough by the same people. I can tell the direction of Finnish dialects pretty well and adapted to my current location pretty well. However the locals can tell I was not born here! My "dialect" is an Eastern blend of a 100 miles circle around here as that's where I used to travel during my 18 year stint as a representative. Locals can tell I'm not local but they can't tell my origins either.
The history of American English is too short for local dialects. The American people have come from all around the world and the process hasn't stopped yet. Even Pres. Trump has a different accent to his parents. Saying that American English is a foreign language for all US citizens may not be too far fetched...
I think you are correct, Bizman. American English has not had enough time to localize as English in England has. Granted, there still exists some subtleties that are noticeable to the keen ear. I live in a fairly large, southern state. On the coast, they have a much different dialect than in the mountains. In between, where I am from, it is different still. The mountain folk drop their R's, the plains folk bend every vowel (like me), and the coastal folk say "wuh-ter" instead of water. Still, if I heard a mountain person I could never say, "Hey, sounds like you are from Boone." I could never pinpoint a town.