Those stories seem to go one of two ways for me. Some writers lean really hard into the caretaker angle, almost like they're writing baby animal rescue content with a ninja backdrop. The bonding becomes a series of domestic scenes: Naruto trying to feed it milk, building a little nest in his apartment, that sort of thing. It's cute, but it can flatten his character if it's not careful—he's not just a gentle soul, he's a lonely, loud kid who might be clumsy about it.
The other path I see more often, and the one I usually click on, uses the kit as a mirror for his own isolation. The bonding isn't just cuddles; it's Naruto recognizing another creature being hunted or feared, and making a promise to protect it that he never got. The best scenes for me are when the kit's vulnerability forces Kurama to interact, creating this weird, begrudging three-way dynamic. It's less about immediate trust and more about laying the first, fragile stones of a bridge that took decades in canon to build. That potential for an accelerated, quieter understanding is what keeps me reading those.