“In other words, Neanderthals were humans.”
Zebras breed with donkies, but a zebra is not a donkey, nor a donkey a zebra. Cross-breeds are not always sterile.
Neanderthals were considerably stronger than Homo Sapien Sapiens and, despite Hollywood, there is nothing to indicate they were any less intelligent.
IMHO, their downfall was their women were almost as tough as the men — and participated in hunting — resulting in less children.
Homo Sapiens Sapiens specialized in having babies by keeping women to safer professsions.
Barefoot and pregnant around the campfire made us the dominant species?
I think it’s more likely that Neanderthals died out because their crazy muscular bodies demanded a lot of calories — more than 50% more than a modern human does. So in times of famine or bad weather, they couldn’t find enough food to keep those muscular bodies fueled. Also, while they could sprint faster, we’re better at long distance running. So we excelled at hunting in non-forested areas.