In most societies, males are typically sent out to war because males can easily have more children than females since they don't have go go through a period of pregnancy, so a society that sacrifices its males on high risk high reward activities can rebuild faster than if it sacrificed females instead. This is why typically you see male soldiers, raiders, and explorers.
But as a result, more warlike societies tend to have less males in the population than females because the males keep getting sent out to die. Remaining females now have less potential mates to choose from, so polygamy becomes socially acceptable to ensure more people get a share of the economic rewards those surviving males bring back.
So you could easily flip this around and say that it's not polygamy that causes war. Rather, war causes polygamy, and polygamy is a reward for the few male "winners" that survive to bring home the loot because now they have less genetic competition.
This model of warfare reducing the proportion of males could also explain why most societies have tended to be patrachical. Scarce males means each males has more bargaining power. In return for the economic loot they bring back, they could demand more say in the household than their counterpart or counterparts. Stretch this population imbalance over a few centuries and you get a patrachical society.
Incel anger is a real thing, but incels are not building warships or running munitions factories.
But you are right, I should have mentioned that high status men contribute to wars as well.
Re incels, it depends on the definition of the term whether they can be regarded as such. I think that the term is most commonly used to refer to a specific group of men in western society which by and large is still monogamic, so it's not very comparable to a mostly polygamic society and the effects it has. I think most men or women who identify as incel can find someone if they really want to, they might just not live up to their standards. I mean, here in the west there is no effect which removes far more women from the dating pool than men :).
I see both monogamy and preventing cosanguinity as examples of actions that could increase this mixing.
Maybe we do need to move to adopt polyamory, the evidence from online dating suggests we are reverting instead to default primate behaviour.
The traditional form of polygamy comes from the natural forces of nature, not oppression.
Given the current state of technology, it is fairly easy to know who is the father of a kid.
Personally, I do not feel the drive to polygamy, in particular because I think it is very emotionally demanding of all the participants and ultimately exhausting and unstable.
I don't know what the "natural forces of nature" are, but of course many, many animal species do not establish monogamous relationships and they still manage to surivive.
...or even own child, especially if there is a pension system and centralised care system.