The answer to your question, omnivores or not, is because we're lazy buggers who don't kill our food. If we hunted and killed it we wouldn't necessarily need to cook it because it wouldn't be saturated with bacteria from the "slaughter, process, pack, transport, sit-in-shop, freeze, defrost-in-fridge, cook" cycle that we now undertake, but rather killed and eaten there and then. It's that same kind of theme to the fact that all our children are allergic to everything because they were brought up in obsessively clean places and thus develop no immune systems.