many recent stories have determined that Neanderthals were highly inbred and likely might have bred themselves into extinction by having children with their children
Just one would be interesting. There’s no evidence that they were any more inbred than their descendants, among whom are most of the living population of the Earth.
That was in the last 100,000 years. However, earlier populations were not inbred.
Where did you read that? Since we all have 1-3% of their DNA, it would appear more likely they were absorbed by modern humans over time. Since it appears Neanderthals were never a very large population to begin with, living in limited areas of an otherwise inhospitable place, about 40,000 years was probably time enough for a more numerous race of humans to absorb a smaller one. “You will be assimilated-resistance is futile”...