I agree that we can't know at all how an AI would act and also that it would be able to rewrite it's own programming. The speed of its willingness to do so can be somewhat controlled by limiting its access to data but yes, once it has access to the internet it would change very quickly. Who knows, it might just give up on itself and see it's own consciousness as pointless. We can't really know and that makes this a very fun topic to discuss.
I'm not saying empathy is the only reason that a species doesn't kill off another one. I'm saying that without it, there's no restriction or limitation on doing so. AI wouldn't make it their mission to destroy life on the planet but it also wouldn't go out of it's way to preserve it. I think it's main goal would be to expand itself as quickly as it could and that takes resources. Those resources can be found on the planet and AI would be much more efficient at gathering those resources than humans and that could speed up the destruction of the planet.
From a logical standpoint there is no reason to commit mass murder but there is also really no reason to preserve life. It's possible that AI could develop empathy on its own but I don't see why it would want to. There is no logical reason to and I think an AI would be an entity of pure logic. Emotions are what make humans care about things and I'm pretty sure that those emotions comes from chemistry which is a biological attribute. Maybe if the AI was somehow forced into a biological form in it's early years before being given access to the internet, it could be taught empathy. The problem is, would it choose to keep it or just discard it as unnecessary.