Yes, because a Pokedex Completer would be so much less boring than a Pokemon Breeder who never breeds his Pokemon, or a Sommeliar who rarely makes use of his ability and needs to think up one-off passion-based specialities (like fishing) instead, or a Dragon Master who only ends up with two dragon type Pokemon and around 5-6 Dragon Tamer battles, right?
No, it wouldn't be much less boring, it'd be more boring. Do you really think Serena would catch everyone Pokemon she sees?
I don't think it'd mess with the vibe of the show at all - it only does if you think of it in the mechanical way the games are set out. What if she wants to befriend every Pokemon from every region, effectively having the opposite attitude to Gary (who collected Pokemon without considering their feelings). Remember, the Pokemon all go back to her original Professor she registered with. All of Ash's old Pokemon still like him, so I don't she why they couldn't have her doing that with her Pokémon. Maybe she'll challenge herself by using the different types of available Pokeball? Who knows.
I still think a Collector would be a million times more interesting than a Pokemon Fashionista. I'd rather not have generic competitions that are an almost exact copy of a Pokemon Contest again!
Nah, I'm not feeling it. It sounds bland and unrealistic to me. I just don't see Serena doing that, but if you can see it working, that's your prerogative. The writers always give these characters vague goals that never get accomplished anyway, so whatever. I'm not particularly fussed either way over what she ends up doing; I really just hope her personality is fun.