I believe it happened over decades as the Irish, Germans, Scottish, and eventually Eastern Europeans came here and mixed their words and pronunciation.  It's been happening in the border citiees like El Paso over decades. I've heard the weirdest Spanglish come out of there.
The different regional accents are there; an untrained ear couldn't tell the difference, though. I grew up near New York City and can tell the difference between Boston, Conneticut and Long Island. Now I've lived in the South and married a Southerner, so I can hear Carolinian, Charleston, Georgia, Gulf States, Cajun, Kentuckyan, and Texan. I might also add that Southern has made its way into my speech, though a Southerner could pick that out in an instant.
To me a British accent sounded the same until I became a Beatle fan and learned about Scouse in Northwest England where Liverpool is. If you hear the early Beatles talk, they sound either Scottish or Irish, but then their accents sort of settled down into "British", probably as they toured the world over 7 years.
I read somewhere that because of the globalism, the Southern accent will probably disappear in the next century. I certainly hope not.
On one YouTube video Paul McCartney spoke with an American accent. I had to laugh; he sounded more like a Cajun.