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You are good at lowering the probability I give to this hypothesis, and I thank you for that, but it is stil not 0.
First about the second point - my point is more like selective advantages do not mean the fitness of the group, or even the fitness of the parents to be maximized, but solely that of the propagation of the gene in descendants. So, from that angle, a gene killing some parents but still making an animal more sexually succesful can still confer a selective advantage. Depending on the ratio of this two of course. My point is precisely that on the whole it can be hugely destructive for the group.
Of course, and now back to your first point, this weakens the group. This would happen with a spiky back but here is where my metaphor stops being useful. It is intelligence. It begins with the ecological dominance - social competition model. The group was all right before intelligence. Surely a weaker but smarter group can compensate for the group level weakening?
My point is pulling an Occam here. Our best hypothesis is that an unknown factor X launched a runaway IQ based competition inside the hominid species. What if factor X is intelligence itself, basically it killing mothers, thus making the sexual competition of males more vivid? Surely such a reduction of factors is worth pondering? And as a side-effect, whatever group level weakness it would cause wrt other species, they would resolve that because of this intelligence, which according to EDSC was not formerly necessary, but at this point became useful for keeping other species at bay?
And if this all at least sounds not-impossible enough to invest resources into pondering or testing, it could generate a Great Filter hypothesis, namely that intelligence needs to be advantageous for the offspring but at some level harmful to parents (dangerous birth, maternal care) to launch such an arms race, it would basically predict that any alien species without the special difficulties of Earth mammals and their problems of pushing a big head through a vagina would not have this arms race.
I'm not sure, but I think your model assumes intelligence is mostly (entirely?) useful for males. Actually, females also have a complex bunch of roles, since they need to take care of themselves and their children and make alliances to get help from both males and females.
You might be interested in Mother Nature by Sarah Hrdy.