>only female Neanderthals transmitted their genes down the Sapiens gene tree

That would be right if the only genes a man passes to his children are on the Y chromosome, but a man passes 23 chromosomes to every one of his children. (One of those 23 will be either an X or a Y.)

Eh, I'd keep "that Y-line just didn't survive the last N0,000 years" as the default assumption.

Just out of curiosity do you know if the Neanderthal mitochondrial line survives in humans today?

Given how human babies are already at the maximum size a human female can deliver, I suspect you may be on to something. Other species don't have such traumatic births, but human babies barely fit through the birth canal. Neanderthal babies were probably much larger. In particular, their skulls. If a Neanderthal male impregnated a human female, I wouldn't be surprised if it killed her. Conversely, a Neanderthal female probably had an easier time delivering a hybrid baby.