I think it all comes down to the general voter. People like "Kubo" but "Zootopia" was more successful to an insane degree ("Kubo" made 70 mil worldwide, while "Zootopia" hit the billion), which means it was simply seen by more people. Already an advantage.
"Kubo" may have a sweet story and inventive visuals, but "Zootopia" has this whole RELEVANT MESSAGE thing going for it, which should especially help it in the current political climate.
And it just seems like a more traditional winner. Laika movies have never won here before and I'm not entirely sure it's gonna change this year. The BAFTA stat is interesting but stats are becoming significantly less relevant with each year. And the "Cars"/"Happy Feet" comparison doesn't really work for me in relation to "Zootopia"/"Kubo" because the 2006 cartoons were both very successful financially and were both met with good, but not great reviews. This year both movies got great reviews but only one killed it at the box office. While also having the message element to it.
As for your question about an animated movie winning the Oscar with less nominations that its direct competition - well, your own example with "Cars" and "Happy Feet" is the answer. "Cars" had 2 noms, "Happy Feet" only had one.