Even though this is a 'new' theory on why/how the Neanderthals vanished, the most accepted one right now (to my limited knowledge) is that of brain formation. It is based on the frontal lobe developments in early man. Without the right tools and thinking skills ANY race is going to vanish in the face of challenge.

But the Neanderthals were around for almost 300,000years, if I remember correctly. That doesn't disprove your theory, but it certainly puts a damper on it.