It's called the Mid-Atlantic or Transatlantic accent and was designed as a way to blend the American accent with British Received Pronunciation. It was deliberately cultivated by the upper class and actors in the early 20th century; there was a book called Speak With Distinction that taught people how to speak like this.

It started dying after WWII and was basically gone from the media by the late 60s. Maybe because post-WWII America was less dependent on ties with Britain for its national identity, or maybe because people decided it sounded silly and fake. No-one spoke with the accent naturally, so it really only took a fashion change for it to disappear.

https://en.wikipedia.org/wiki/Mid-Atlantic_accent

https://www.atlasobscura.com/articles/how-a-fake-british-acc...