Because Liz does not approve of genocide, even of the enemy?
It works better if you consider "Elizabeth Ngo" as a set of character traits, and the Thirteen as "Elizabeth as a Cylon."
Liz-as-a-Cylon is loyal to
Cylons-her people, just like "Human Liz" is loyal to Kowloon.
because her central 'virtue' is loyalty to her
People. Original flavor Liz is loyal to Kowloon and Humanity. The Triplets are loyal to New Circe, and Thirteen is loyal to the Cylon Race.
not to their politics or priorities, but to the 'race' as a whole-all three of her are focused in one way or another on the goal of preventing extinction. All three versions of her (Liz, The Triplets, and the Thirteens) are rather ruthless and calculating, with a belief that 'some must be sacrificed if all are to be saved'.
because that's as central to the
entity as her/their intolerance for corruption and incompetence.
Each of the three aspects, is rooted in a sort of 'inner' moral dogma, which puts that which they are loyal to ahead of themselves, all three versions are to some degree, intensely political in nature-but not 'courtly politics' so much as 'mob don politics'.
Thirteen's banishment of the Ones was not due to their desire for Genocide, but rather, the incompetence of their long term planning. If she could exterminate an entire people yet keep her own people (Mostly) intact and fully viable to rebuild, that is what she would do-but there's the 'business' sensibility of not wasting what you do not have to. To fully extirpate the Ones and discredit them, she arranged for them to have the best chance to redeem themselves-knowing full well they would fail utterly.
Because she had no belief in the content of the Ones collective character. (A poor leader and poor followers by extension, as shown by his/their incompetence at a plan guaranteed to succeed.)
The Triplets have perfect confidence in their Humans, New Circe, and the AI intelligences resident there-direct intervention was only needed to keep the single Cavil in custody. (Hence, only sticking to racking up a kill count at the special holding facility, and then only because the defenses were pointed the wrong direction.) also, at least one of them is an outright psychopath.
clear? Thirteen isn't even BOTHERED by Genocide-if it's competently executed. (convincing her of competence is kind of difficult, she tends to see extreme measures like Genocide as a sign of other forms of incompetence and finds incompetence intolerable by definition, but THEORETICALLY...)
This is shown in her point about the Cylon Colony being a weakness and fuming at the fact the Ones left it a weakness instead of establishing backups.
In all her versions, (originals and copies) she has a keen belief in Entropy and a driving need to resist it.
In a sense, you can pick this up from Elizabeth's moves on her own; She took in hunted refugees and incorporated them into her system, established Universities and 'second chance' academies, rebuilt first her homeworld's economy, and then set about revamping and rebuilding the economic base of her home region of space, forced diplomacy through, all to resist collapse and the impacts of social and economic entropy.
this comes from growing up knowing that Entropy had her by the short-hairs. That impending sense not only of mortality, but of unfairness, mixed with a belief that she needs to do
more. This all carried through with the Thirteens-but with a focus on the Cylon 'race' or
people.
The way the Cavils had been managing the war, is in her eyes a constant march of 'almost successes' mixed with outright failures. They killed the humans of the Cyrannus system, but in the process rendered the prize worthless, they hunted the survivors playing cat-and-mouse head-games instead of delivering the final blow, and made an enemy that consistently proceeded to beat the silicon snot out of them at every encounter. Cavil grasped for more control and made worse mistakes with every grasp for that control, driving further and further into
defeat and Entropy (signified by losing better than half his siblings entirely.)
To her, she needed a humiliation that would prevent him from regaining influence once he was deposed, because she sees his errors as grave symptoms of impending collapse.
her view is longer-term than her estimated survival under optimal conditions; she intends the Cylon people to outlive the GALAXY. that's her 'horizon', and it leaves room for others to coexist...because it's more efficient than trying to exterminate them.
