People have fought for a number of reasons, material resources AND reproductive resources are usually key to those. Historically, raiding for woman and resources has been a constant. A big tribe is a safe tribe, more women is key. Even in modern times, you can see the pressure in expensionist/aggressive societies for women to have more children.
Fighting for reproductive resources is, however, an outmoded concern. While some states are fighting falling birthrates, none have went to war to acquire more women in recent times. And the reason why states are pursuing population is, again, material.
Evolutionary biases are also essentially irrelevant in how societies are structured. The structures of societies are very intentional and based on material reality, not mere biases.
Generally, men have mostly done the fighting, especially in wars of aggression. The reasons for these are material, as men are often better at fighting. It's not to protect women. When it's useful and makes sense for women to fight, then women fight.
Evolutionary biases are fundamentally relevant to the way society is structured. Historically more violent behavior in males has always been very adaptive as the rewards are far greater.
Put another way, if you took almost any society today and made everyone women, you would not see a major decrease in violence, as the vast majority of violence done serves structural and material reasons.
I agree with your second point though.
https://en.wikipedia.org/wiki/Women_in_the_military
And even then, they were support, not infantry.
This generally doesn't happen unless either the society is quite rich but lacks strong men, or cases of emergency, or if there is surplus of land and food, because raising armies is very costly, and as a result it doesn't make sense not to send the strongest fighters possible as it is expensive to outfit them and to maintain production at home.
Nowadays, women are proving extremely competent as fighter pilots as their bodies are better at withstanding G-Forces, but in classical infantry where there is a large strength requirement again it doesn't make much sense.
Likely coming from being shorter. The heart doesn't have to push the blood as far uphill.
Women do indeed fight, but not until it gets desperate.
It's true that women generally don't fight until it's desperate historically. I explained why in the comment you replied to.
People fought protecting material resources. Reproductive resources were only useful insofar as they help you produce more subordinates to generate more material resources. In feudalism this meant that reproductive resources were very important, but in slavery and capitalism it isn't really the case.
Given the realities of military engagements in Feudal Europe - and the rather small army sizes - its not true that sending women to war would cause a fatal decrease in the birth rate, at all.