The Transatlantic (or Mid-Atlantic) Accent, explained.
The Transatlantic accent isn’t British, but it also isn’t American. In fact, it isn’t from anywhere, but it’s made to sound like it could be from somewhere between here and the UK (Mid-Atlantic, get it?).
Essentially, back in the ’30s and ’40s, wealthy people (especially on the east coast) decided to adopt this hybrid accent as a “class” marker. “Hah-vahd English” or “aristocratic drawl” might ring a bell. Rich people taught it in boarding schools, finishing schools, and you guessed it, in theater and drama classes.
While we can assume Kelsey, the actor (who, to be clear, speaks totally normal American English), developed his Transatlantic accent, along with the many others he masters, in theater school, his character, Frasier, probably picked it up from one of the many snobby private schools he attended in Boston. Notice how his dad, who is of a perceptively lower class, doesn’t speak in the same way.