[Symmetry]

That's probably more a matter of natural selection. neanderthal y-chromosome DNA was also almost entirely eliminated from the human genome, as well as neanderthal genes in several other places.

When two different dog breeds have pups those mutts are just as fertile as any other dog. When a horse and a donkey have a mule that mule is almost entirely infertile. The first human/neanderthal descendants were probably significantly less fertile than their parents but generations of selective pressure seem to have purged the particular genes that were causing problems which you would expect to include mDNA.