2) Yes, exactly My point wasn't that pokemon wouldn't willingly battle or that having those pokemon exist is wrong. It was that trying to avoid the issue by making all pokemon want to battle despite the fact that, statistically, there should be plenty that don't, is a common mistake of convenience in OT fanfiction, where things simply work out nicely for the protagonist.
By not assuming it's an either/or situation.
Wild animals raised as pets cannot be put back into the wild. It's even more impossible for domestic animals. You've made them so they can't live on their own, and you now have a responsibility to care for them.
That said, using the fact you have to take care of them and that they cannot survive on their own as justification for being able to do whatever you want with them is wrong. A pet cougar cannot be returned to the wild. This does not mean that the man who decided to keep it in his small apartment was not doing something wrong. Similarly, that a pug should be kept as a pet and not abandoned in the wild does not mean it was okay to keep a young pug around as a chew toy for a larger, more aggressive dog.
Captivity is not a catch-all term. Confining an animal in a small cage is obviously different than confining them in a large park. This isn't a simplistic right/wrong, captivity/freedom bit. If you'd take a few breaths, consider that Lucki's pokemon serve to explain the facets of the situation.
Silver is a bred pokemon who is socialized with humans and is frightened by battles. She's also a newly hatched infant. She'd like being someone's pet, especially if there were other squirtle for her to be friends with, and wouldn't mind being a contest pokemon. However, with Lucki she's been forced into situations she doesn't want, and is trapped because, by nature of her bred status, she can't leave. Even if she could run away or demand release, she has nowhere to go. In the end, Silver has had a breakdown, is clear that she is only there because she can't leave, and Lucki sends her out again. Lucki didn't create the situation Silver is in, but she took advantage of it rather than caring about Silver.
Flare has absolutely no problem with battles. He's also socialized with humans. Lucki is neglectful and emotionally abusive of him. The problem is how she treats him, not the basic situation. He would have been happy belonging to someone like the Team Magma boy, who actually wants him and would pay attention to him. Flare doesn't simply run off. He leaves for another trainer who will treat him differently.
Raiden is a child. He belongs with his family, who have been left without knowing if he's even alive, and although he doesn't mind battling itself, he's too young to be able to take the brutality of many upper-level battles. Perhaps as an adult he'd want to belong to a trainer.
Saurius is an example of pokemon that has other responsibilities and goals. He has friends and family, and ones that need his protection. He simply has no reason to want to be with a trainer.
And the absol says that she does not want to belong to Lucki. Responding to a pokemon clearly expressing its wishes with "oh, you're just stupid, you really do want to belong to a trainer and just don't know it" is no different than saying "that's nice, but I don't care", only with the added bonus of being insulting while you do it.