What they did with Claire and Amelia in later seasons feels a little bit like a retcon.
Claire is believable. Trauma changes people, especially children. When we first meet her, she’s quiet, timid, polite. But after losing both of her parents, she lashes out at the world, at Castiel, at her mother and the forces that took everything away from her.
Amelia is different. She is someone grounded in reality. Despite witnessing with her own eyes that Jimmy’s hand was completely fine after being submerged in boiling water, she doesn’t let herself slip into the belief that it was a divine miracle. She begs Jimmy to get help, no matter how much he tries to explain. When she realizes her husband isn’t going to budge, she makes an ultimatum to take Claire away, believing him to be a danger in his current state.
When Jimmy comes back a year later, we find out they’ve stopped looking for him. Amelia isn’t all that sympathetic towards Jimmy. She is angry that he never kept in touch. She doesn’t allow him to see Claire. She says their relationship can’t be the same. Very reluctantly, she allows him to have dinner together.
Now, after their neighbours get posessed, we aren’t sure if Jimmy was actually talking to Amelia or to the demon. “Amelia’s” insistence that they can’t split up again hints towards the fact that the demon might have been trying to keep Jimmy close so they could grab him once the Winchesters drove away. This is further supported by the fact that the demon then slaps Claire in anger and points out how “it’s just not my day, is it?” Implying they were trying to keep Jimmy from getting away.
After that, we only see actual Amelia run to check over Claire after her being posessed by Castiel, despite her husband bleeding out on the floor. Now, you could make an argument that she was frozen in fear at the sight on an angel posessing her daughter. Understandable. Yet, when Jimmy is re-posessed, Amelia makes no move to chase after her husband, try to get him to stay, talk to him again. If you believe it was truly Amelia, and not the demon, who said they shouldn’t split again in that car, those actions make even less sense. Plausible deniability here is that, once again, seeing an angel in the flesh is very intimidating. But alternatively, that could mean Amelia has moved on. She’s accepted the fact that Jimmy is gone. He was not the same person anymore, and chasing after him would be pointless.
If it was indeed the demon in the car, that would mean that the last time we saw actual Amelia speak to Jimmy was when she tried holding him back from hammering their “neighbour” to death. She never took back any of her previous words. We don’t know if she changed her mind on giving Jimmy another chance after finding out angels and demons were real.
Now, we flash forward to season 10. We find out Amelia has abandoned Claire at her mother’s. She has been searching for Jimmy tirelessly for years. So long, she lost sight of what was important — taking care of Claire. She is grief-stricken. All she wants is to find Jimmy.
Now, that seems like a very drastic shift to me. Once again, plausible deniability: maybe, after she got over her fear of angels, she realized Jimmy was way too important for her to let go. But we also can’t forget the fact that Amelia from season 4 comes across like an extremely different person. If you asked me to describe what I thought Amelia was doing before we found it out from canon, I would have said she moved away, settled down somewhere quiet with Claire, enrolled her in school, found a quiet job. Maybe found love again. Season 4 Amelia feels like someone who is ready to let go of things out of her control and prioritize what is more important to her, mainly Claire and her wellbeing.
Of course, season 4 Amelia is a character that appears very briefly. There are many holes to fill with her character, and the writers did just that by giving her a different path to follow than what we may have expected. It wasn’t a wholly unbelievable route for her to take, but it also wasn’t entirely supported by what had already been established for her character. At least in my opinion.
I think Amelia had some really great potential. It really is a shame she was killed off so easily for the crime of being a woman on supernatural. I would have loved to see her try to repair her relationship with Claire. To speak with Castiel about who Jimmy was, properly grieve his loss. Instead, well. We got what we got.