I mean, a race of people that live by stealing the lives of others? Unless they can choose to live off of animals instead of people, I see no reason why bringing them to extinction wasn't a good idea.
The phoenix might be a topsy-turvy asshole, but she made the right call here. Countless lives would continue to die off before none would be left, leaving that race to possibly steal each other's lives before snuffing themselves out. There would be no life left at that rate.