We agree right that we both already know Neanderthals died in many diverse ways? I certainly take it that you think they died from disease, murder, starvation, accidents, animal attacks, and even raids from other groups (even that!). I take it you think all of those happened plenty. I do also.
About the fact of diverse causes of death, I think each and all of us agree to that. The only contention we seem to have I'm aware of is whether our Sapien ancestors routinely killed Neanderthals (and regardless of whether that was individual murders, group on group attacks, or even organized campaigns under a leader, any of these).
I'm guessing obviously without extensive evidence that they did, and you that they did not. Right?
The reason I favor the hypothesis our ancestors routinely killed Neanderthals is that we did it to Native Americans, and to wolves, etc., etc.. And before that, to each other in Europe extensively and nearly continuously for centuries at a time until the recent Pax Americana.
I'm thinking our ancestors were much the same species 45,000 years ago as we were 3,500 years ago, and we know that constant war for territory is only historically normal 3,500 years ago.
Only broad alliances and the recent spread of the "rule of law" idea and the United Nations have tamped down war to a degree, slowing that chronic tendency to war down somewhat into a quieter equilibrium....or at least for a while. Could change.