Yea we did. We found out about the story between him and his brother, and how he got Tonraq exiled to the South. He had a pretty clear motive, no matter how stupid sounding it was. "I must release Vaatu to blah blah blah KAIJU BATTLE!!"
I mean, it's much more than we got for Team Z. Just a group of powerful benders that want to kill the Avatar. No back story on how they got together or what exactly drove them to come to the conclusion that the Avatar cycle must stop, just some shit said in passing about Zaheer rescuing P'Li from some war lord and their past attempt to take Korra.
Kuvira falls in this too. "Hey look at me, I hate my mommy, taking over the Earth Kingdom, and turning into Sams Club brand Hitler with a beauty mark and hair."
No, I would catergorize that more as a
goal rather than a
motive. A goal is what you want to achieve, a motive is why you want to achieve it, and we didn't get anything except "Because it's
spiritual, guiz" which is a meaningless term in LoK, so it's no motive at all.
Similarly, the background of the Z team is not motivation of the Z team. Background might inform the audience how they came to form that motivation, but it's not necessary for them to have motivation, which is made explicit: They believe that the world will be better off in a chaotic society where freedom is abundance, because they think Kingdoms and stuff suck because of corrupt rulers.
As for Kuvira, her motive is muddy, like you said.