As a Cheers spin-off series, Frasier featured all of the main characters from the original iconic NBC sitcom — except for Kirstie Alley's Rebecca Howe. Following an 11-season run, the Boston-set series Cheers came to an end in 1993, but the project was still very popular; this lead the network to capitalize on the public's continued interest in the series with a spin-off: a show focusing on Kelsey Grammer's character Frasier Crane.
Joining Cheers later in its run, NBC brought Alley into the sitcom as a replacement character for Shelley Long's Diane Chambers. By season 5, the original cast member decided to walk away from the show with the intention of wanting to pursue a movie career. Cheers was able to find a good excuse for her exit, but they were left with a gaping hole in its ensemble cast as Diane and Sam Malone's (Ted Danson) relationship was critical to the series. That's where the character of Rebecca was born — however, knowing that she couldn't be a Diane copycat, they changed up the role to be a bit less buttoned-up, more spontaneous, and fun.
It eventually became clear that a romantic dalliance between Sam and Rebecca just wouldn't work, so the idea was dropped altogether, partnering her up with recurring characters instead. That said, she still became an important part of Cheers' ensemble, and while everyone missed Diane in the pub, the show's popularity further soared until it ended. Rebecca also got her own set of fans who were drawn to her more eccentric charm, so why didn't NBC bring her back to appear in Frasier like the rest of the Cheers' gang?
Rebecca's lack of guesting in the Seattle-based spin-off wasn't because the broadcasting network or the Frasier executives didn't want to feature her — it was Alley's decision to not appear in the award-winning sitcom. The decision was a personal choice from the actress that stemmed from being a member of the Church of Scientology; Alley was raised as a Methodist but became a Scientologist in 1979 and remains one to this day. Before she was even invited to make an appearance on Frasier, Alley announced that there's no way that she's partaking in the project as recalled by co-creator and executive producer David Lee. This was because the sitcom centered on the medical practices of psychiatrists Frasier and Niles Crane (David Hyde Pierce) — a field Scientologists do not believe in it. According to Lee, he wryly responded "I don't recall asking."
In terms of narrative, there's really no compelling reason for Rebecca to visit Frasier. Unlike the other Cheers' character who either visited him in Seattle or he met up back in Boston during Cliff Clavin's (John Ratzenberger) retirement party, there was never much one-on-one interaction between her and the psychiatrist-turned-radio host. That's due to the timing and nature of Rebecca's introduction in Cheers. In any case, had Alley not vocally express her lack of desire to appear in Frasier, perhaps the writers could've found a way to incorporate her in the sitcom just for fun.