Infanticide was common in premodern societies. Visibly deformed infants were almost always killed. It is an error to ignore that factor.
If they could not produce viable genetic offspring then there is none. This does not mean that Neanderthals and Humans had the occasional roll in the hay or even that there were long ternm stable relationships between the species.
No, it doesn't. Hell, it doesn't even mean that Humans and sperm whales didn't partake of the occasional roll in the hay or even long term stable relationships, but still, they probably didn't.
If you are going to be ludicrous leave the debate. Humans and sperm whales have never shared hunting grounds :)
Your wrong visibly deformed children are not always killed in Hunter Gatherer cultures especially those cultures in very rich environments such as Western Europe. You are getting your evidence of this practice from African H&Gs living in very marginal environments.
Also how do you know what Neanderthal societies did with deformed children? I mean you are the one that keeps saying they were so strange we can't even understand them.
However I can show ample evidence that cripples and the deformed were cared for in cultures at the time from the fossil record. Hell Neanderthals were known for caring for their crippled and deformed members.