I don't agree with your 'very' in the last sentence.Dialects develop from locals making a regional adjustment.
Early Modern British English developed at the same time that American English was created American English was not 'created' (though some American spellings were introduced by Webster) and developed. It is actually impossible for them to be dialects. That, frankly, is nonsense. British English would have to have come first. It didn't. Well, actually the English of the 16th and early 17th centuries did 'come first'. They developed in parallel and then went in very different directions directly related to the development of the prospective countries.
The argument that BrE would have had to have 'come first' for BrE and AmE to be considered dialects is nonsense.
Today I cannot understand Swedish. Modern English and Swedish are two different languages.
Some centuries ago, my ancestors would have understood the dialect of the ancestors of modern Swedes. Early forms of English and of Swedish were different dialects of the same language.
The ancestors of these people would have understood the language of the ancestors of the modern-day speakers of French, and so it goes on.
Had it not been for radio, film, television, the internet etc, AmE and BrE might well have developed into two mutually unintelligible languages. But that is not what happened.