It seems like that's more like what you're doing; reading between non existent lines to reach some headcanon that views Ayane as better than she is.
This conversation isn't even about Ayane being "caring", it's about her being empathetic. That's not the same thing. I recommend googling the definition of empathy.
Ayane also literally says she was out of ideas:
"Ayane's card" was literally Chika's idea.
You're right that Nodoka isn't empathetic. She doesn't understand others. She still cares for her mother and friends, though, hence Empathy and Caring are not the same thing. Being nice or kind isn't the same as understanding others. Sympathy vs Empathy. Etc etc. Ayane also didn't understand Molly on the beach btw, I've brought that up in another post (The Noriko being more perceptive part):
Ayane's lack of empathy contrasts her with Noriko.
But yeah, their relationships are dysfunctional. It'd probably be better if they quit lying to, hitting (in Ayane's case), and betraying eachother.
It is one sided from Ami's side, though.
Keep in mind: Ami is broken in bed right now. Where are her "friends" that she's been there for when they were sad? There's a reason Ami pointed out that she wishes she had a friend she could trust last update:
All of her friends seem to want to betray her and fuck her uncle. Also apparently fuck him on her bed, because I guess that's just the kind of people they are. Sana at least seems up for sharing, ironically: