I dunno. Maybe I don't like cliched characters whose scenes usually involve speaking in, pretty much gibberish space jargon, and if you think logically has no reason whatsoever to be a member of the crew.
Interesting point of view. It's more often I hear (if Kaylee wasn't the favorite) that viewers simply thought she was fine or mildly enjoyable. However your view is facinating, and it's interesting how just one character can define the take-away of an entire show. I'd love to know more about what affected you most when watching!
In terms of cliched, not 100% sure what you mean. I generally find Firefly to be one of the most realistic feeling, original shows I've ever seen. I will grant you, however, since it aired, many a show like it have tried to capture it's magic, leading to tropes arising from some of it's practices. In terms of the space jargon, I will also grant you that some of it didn't land very well. There were several phrases in the first episode that I was relieved didn't stick around. But the purpose of it was to try and create a realistic world/environment. It's hundreds of years in the future, in an entirely different world/culture. English is far from a dead anguage, and it's always changing. If they were to have used early 2000s phrases and slang, it would have dated the show instantly, and proved itself incompetent by assuming that those phrases were beyond "phasing out". How best to ensure the show stands apart as truly being "from a completely new and original time"? Create new phrases. Sure, some of the words and names for things are sci-fi throw-aways, but I still use "shiny" in day to day life.
In terms of the "having no logical reason to be part of the crew", I'm rather completely at a loss for what you mean. Kaylee, serving as the mechanic, quite iterally keeps the ship flying. She is one of the most important members of the crew. Without her, there is no show. Now, if you had said "River has no reason to be on the crew". Sure. She does not and cannot pull her wait (until maybe the movie), but she still has reason thematically and storywise. The way she and Simon are brought onto the ship makes sense and while she does not offer the ship any physical merit, her presence still benefits the crew in this way and that, and overall contributes to the show positively. Same can be said of the Shepherd, another technically "non contributing member" of the crew. In reality, all the characters contribute positively, wether in terms of the actual crew or simply the story of the show.