As mentioned in a previous answer to one of your questions, this is called Mid-Atlantic English and was commonly used in American films of the 1930s and 40s.
Wikipedia gives the following reasons that someone would use the accent:
- Intentionally practiced for stage or other use (as with many Hollywood actors of the past). A version of this accent, codified by voice coach Edith Skinner, is widely taught in acting schools as American Theater Standard.
- Developed naturally by spending extended time in various Anglophone communities outside one's native environment, most typically in North America and the United Kingdom.
- Learned at a boarding school in America prior to the 1960s (after which it fell out of vogue).
So essentially, this type of speech was never common and was only natural in the case of ex-pats.