Spin-offs are always an uphill battle, and Frasier took nothing from Cheers that made it so successful, i.e., likable characters, humor that didn't depend on those characters' pointless rejection of honesty, and plausible regional accents. On Cheers, Frasier's accent made sense: It's known as a "mid-Atlantic" accent, which isn't actually a real accent.
It was made up for old movie stars so they wouldn't sound like they were from anywhere in particular, and then the upper class of Boston adopted it as their own, along with weird suits and nepotism.
The Frasier of Cheers wore this regional stereotype like a hand-sewn cravat. Still, in their haste to give this character some semblance of relatability, Frasier's writers decided he was raised in Seattle, the least accented place, by a retired cop who sounds like a Seattle cop. To complicate matters further, he also gained a brother who never lived in Boston but somehow also speaks with this made-up Boston accent.
There appears to be an easy explanation: He went to Harvard. Niles went to Yale in Connecticut, where the mid-Atlantic accent is less common but definitely present. But it's nearly impossible to pick up a permanent new accent after about the age of 12, even after decades of living in a new area, let alone a few years of school. Was their mother perhaps a New Englander? If she was, she didn't talk like it.
Besides, a flashback of Frasier and Niles at their Seattle prep school at the ages of 12 and 7 shows no hint of their future accents, if plenty of evidence of their future insufferability.
The only possibility is that at some point, they both put in the tireless work with a speech therapist that it takes to even have a chance of changing one's accent in adulthood. To be fair, that's an extremely Frasier and Niles move.
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