Ah, something will take our niche in the world, and fill in the empty space of random violence and powerplay that is left when we are all eliminated.
Then blow up the planet.
As long as I am not depressed or bitter enough to enjoy things of humans too. And to see that still more goes OK than absolutely wrong, I will vote against the total eradication of humankind. But, Shleed is right, it would be the only effective way of dealing with the nastiness of human nature.
I wouldn't literally want humanity dead, as they are interesting. But if you really care about stopping all the crap in the world, then the only solution is to get rid of the cause of it: humans. Otherwise it'll keep on going.