The Barbarians were always a factor in Roman history, it’s just that she was always better equipped in terms of manpower to field an effective military and social response, but by the time we’re talking about, owing to the decay of the societies morality, so say Nixon, +Sheen and other historians, they were incapable of keeping the political integrity of the Empire intact as it was before, and the outer borders deteriorated.
It’s like a disease which attacks the structure of the bones, eventually, the mass of the body itself is insupportable because of the decay.
That is exceedingly hard to determine in the perpetual soap opera that were the Roman monarchy. It would be easier to say that the fall of the western empire was due to multiculturalism than to moral decay.
It could even be asserted that Christianity was responsible, Constantine I taking over just a little over a hundred years before it fell.