Sure it does. We see cultural displacement in the archaeological record all over the world. Bones marred by marks of damage by weapons. Otzi the iceman was possibly hunted down and smote on the mountainside like the Balrog Gandalf did in.
I’m not saying violence didnt happen, of course it did! I’m saying the evidence is not that neanderthals were simply eradicated like animals that were hunted to extinction and that multiple factors led to their gradual decline over time.