Why aren't there omnicidal Buddhists?

So, I'm not a Buddhist, but my understanding is that in Buddhist thought, existence is the root of suffering, and Buddhists seek to end suffering by attaining a state of spiritual enlightenment that, after death, will cause them to cease to exist instead of reincarnating ("Nirvana"). Since this spiritual oblivion is viewed as a good thing by Buddhists as a result, and that existence is viewed as a bad thing that causes suffering, why aren't there any murderous Buddhists that seek to bring about this oblivion more directly by killing everyone? You can't reincarnate into a new life if there's no new lives to reincarnate into, after all. Even if reincarnating into animals might be possible, you could prevent that by systematically wiping out all life on Earth down to the smallest microbe. However, I've never heard of any Buddhist sects that actively seek to murder everybody. Why is this the case, when it seems like "murder everybody" could very easily be a logical conclusion of the Buddhist belief system? Have there actually been these sorts of Buddhist death-cults in the past, that simply haven't survived to the modern day (presumably due to having been violently suppressed by the governments of the nations they lived in once they started trying to murder everyone)?