Sokai week has got me thinking, and one of my personal favorite moments is in KH3 when Terranort is about to kill Kairi, and Sora runs over and throws himself around her. It's so desperate, so simple-- He doesn't have time for a quip, or to pull out his Keyblade and heroically deflect the attack. Sora just has his body to shield her, and he's completely exposing his back to Terranort; it's like all he has time to think is, 'Take me instead.' It's just such a profound act of sacrifice and love.
Same, that moment in KH3 really got me too because of all the reasons you described. Sora's acting on pure instinct in that moment, and his instinct is to protect Kairi at all costs because she's so important to him. It was also a beautiful parallel to her shielding him in KH1 when he was a Heartless, and then how he also shielded her in KH2 when Ansem the Wise's device explodes. And then of course after sharing the paopu fruit with her in KH3, he takes his promise to protect her very seriously, as the end of KH3, ReMind, and Melody of Memory have all shown.