Saw someone say Inoue appearing twice is proof of how important she is, but that's disregarding the context of what Ichigo's thinking here.
"A time when I felt pride in my shinigami powers...? I can't even begin to count them all!!"
Chad has just urged Ichigo to think of a time when he's proud of his power to act as a trigger/lode stone to activating his fullbring. So Ichigo does.
He thinks of the first time he helped save someone he knew (Inoue), the second time (Chad), protecting his sisters, overcoming those hollows with Ishida and winning him as a friend, of himself saving Rukia, and then...Inoue's wibbly face before, finally, Rukia.
First, the last two on the first page and the Rukia panel are important.
On the first page: every other image is Ichigo's POV, what he would have seen, except for the Rukia rescue. In every other instance he thinks of the people he saved and their face as he did it, but for Rukia he dodges her and thinks of his own joy in the moment. He avoids thinking of her because it's too much and too painful until the last moment, and Rukia's image comes into his mind like a crescendo, and with her his ability to use his power again.
The last image of Inoue is...odd at first glance.
If he was proud of saving her, why that image? There were moments in the Hueco Mundo arc he could have thought of. If it was seeing her at the end, why not the moment he first saw her when everyone appeared after Aizen was sealed when she wasn't pulling a stupid face?
Except, taking into account Ichigo's words/thoughts, his bringing up her face then is when he's looking for moments he ISN'T proud.
Her wibbly face would have been the very last thing Ichigo consciously saw before he was taken by the incredible pain of his loss of power and fell into a coma. He looked at Rukia and everyone else first, then Inoue spoke to him so he turned to her to reassure him he was himself, then collapsed mid-sentence. He has nothing else to associate with that moment, so her face pops up when he's wondering "Even then, even when it caused me pain and I lost it, was I proud?"
It's the same with Rukia on the next page. "Even then, even when my power disappeared, was I proud?"
And in both cases the answer is yes.
The key difference, not panel size or number of images, between Inoue's two appearances in Ichigo's mind and Rukia's one, is that Inoue's, like everyone else, are greyed out copy-paste images from the events in the manga.
Ichigo remembers those moments exactly as they were and they're part of the horde of memories, not sticking out uniquely.
Rukia on the other hand, that's a unique image. It sticks out uniquely for size, but also because that image of Rukia only appears here.
When she disappeared from his sight with the last of his power before TLA she was facing him head on. When she disappeared through a senkaimon as his power drained away under Byakuya's cut to his saketsu chain point, she looked over her shoulder, but she wasn't wearing a shihakushou and she wasn't smiling. This image is a mashup of those two moments as Ichigo finally lets himself confront and absorb all his memories and pride in himself that are tied up in her that are the key to regaining access to his power.
Being in Ichigo's head for these pages, that means this is his fantasy image of her.
Rukia's importance to Ichigo is shown in the fact that he isn't objective about her. He adds a romantic flair to the thought of her. A breeze ruffling her hair as she looks over her shoulder in a cool way that shows off her profile, as she stands in front of a metaphorical senkaimon showing where she is. And she is beautiful.
I don't ship Ichiruki, but I do firmly believe Ichigo at minimum had some degree of deeper feelings for her that he either grew out of like a puppy love, or came to accept wouldn't be returned and was completely content to drop them and continue to be just very, very close friends. Probably that Rukia caught some feels for Ichigo but they either just didn't do anything about it in time, or the moments either of them wanted to the other wasn't yet on the same page or had already let go of the idea themself.
(ie: Ichigo caught on to the fact he could/did love Rukia as more than friends, processed it during the 17 months, then let it go right after TLA, while Rukia had no time to breathe between her lieutenant promotion and the wars and only caught on after tybw, but decided not to pursue it because Yhwach's threat and having Ichigo as a friend is better than acknowledging it because he would walk away permanently because of Yhwach's threat. But low-key they're constantly in a state of "give me one day, one conversation about it and you'll convince me" because they don't/can't love the people they ended up with.)
