Your genetic influence isn't gone in 6.8MY, just because the genes aren't the same doesn't mean you aren't the source (and you have many genes that you share with other humans, many of which will be conserved through evolution), which is really the thing they want, they want to be the source because according to them, they're the better male.

I think these dudes and fascists/neo-nazis have a similar outlook on heredity. They seem to think that your gene pool is highly important for your success, very eugenics tier thinking. They want to be part of this perfect gene pool, so they can use their ancestors as evidence that they'll also do great.

Biologically, men should sleep around. Like you said, 50% influence, so not each kid is going to be the same. Statistically, you'd wanna have about 4 to ensure most of your genetics is passed, but no human thinks like this. Most dudes think spreading genes = alpha neanderthal move. They conflate our ancestral archaic humans with their image of this badass and fit hunter, when in reality most of our ancestors were eating dandelions until they figured out how to work together. So that's what they wanna be, they wanna spread their genes that way, ignoring that women gestate for 9 months, and most likely want men who will help raise the kid. What's the point of siring so many kids, if you don't even see that they'll succeed? Unfortunately, their child brain convinces them their genetics is enough for success.

Your last point is really the one that matters. Ignoring the genetics and evolution, why would you want to "spread" genes that you don't even know will stick around, when the consequence is always damaging a woman or her future child's life. We all know what they think about women, so it's not surprising.