She does have a virtue counterpart. Or, at least a rival. One of the Eight-Virtue Virgins who I just introduced, Decna (Goodness).
Sort of like in Greek mythology, how Ate was the Loki-esque mischief-making character, moving to and fro with lightning lickety-quickness, and the humble daughters of Zeus, the Litai, weren't nearly as fast, and thus were always playing catch-up with all the havoc she left in her wake.
Khadai is purposely stronger than Decna, but the two are counterparts. Each side has nine players, with Uburra-Namall as the neutral, just as you suggested. And in all truth, she tends to lean more in the good direction, giving the good side the advantage.
It's a philosophical statement.
“…Judge not what a man has done, but judge what he could have done if he was a different bloke altogether. For art thou a leper? And a leper can changeth his spots…” --Rudy Wade, Misfits (Series 4, Episode 8)