The short answer is that the different American accents are partly due to settlers from different parts of England (yes, and the rest of the world). The British Isles has a huge range of very distinct, very strong accents (even dialects in some parts).

So you have a bit of London mixed in with a bit of East Anglia, mixed in with some West country, etc and scattered across the US.

But, these accents were exported several hundred years ago. So, the sounds on both sides of the ocean have diverged, and the accents are no longer a neat match.

That said, there is a remote fishing community somewhere on the North Eastern coast that has an accent that is understood to be very close to "Shakespeare's" English (that is, from around Stratford in the late sixteenth, early seventeenth century).