if the principle concern is survival, it will remain so until there is time to breathe and establish a social order. While the women in this story are history students, they are first and foremost people concerned with their survival, not the potentiality of a patriarchy.
How do you argue "their principle concern is survival", when there's a professionally trained army, a safe manufacturing base, a supply line for the army, etc. These people aren't all hunting for their next meal. They've already started to form clear division in labor - which in time, will solidify into caste, class, social prestige, etc. If these women continue to only do the things they used to do in their old patriarchal society, then this newly born civilization will turn into a patriarchal one, and much faster than actual history, too. I don't have to guess, this is how actual history played out.
even if the women had more influence in the group (and/or time for consideration) I would not move forward with the supposition that they believe a patriarchy to be an eventuality of the group they are a part of. Perhaps they hold different beliefs about the future of the group. It's important to frame their actions with this thought in mind.
These people are acting only under the directives of one mind - the author's. Although the author's a man, I don't simply assume his natural lean towards patriarchal tendency based solely on his gender. No, I judge his preference based on all the tiny details he's been presenting in the story thus far - how female characters are portrayed, how they acted, what they did and said - and the conclusion is clear: It's going for patriarchal society, with a side of belittling women at that (why are these women so incapable???).
The likelihood of a few history students being able to create sophisticated weaponry to equalize the playing field is highly unlikely. Bows, arrows, swords, etc. all require strength and skill to use. Since these are the weapons of the time, human strength becomes important. Although these women could take up arms, they would still be reliant upon human strength. Utilizing animals to fight, however, is a way to tap into a different kind of strength. Thus, I don't think breeding animals to be useless at all.
There is also the question of time. How long would it take to make these weapons? How much would it take in terms of resources, cooperation, and effort? This would delay the utilization of such weaponry significantly.
Deep knowledge is an inhibiting factor. I can know about a tank but I can't create one. And even if we dial it back to explosives or a simple gun, that's still complex weaponry. It requires an understanding of the mechanisms that move it to function, and the principles of designing/crafting it.
A few history students vs. absolute cavemen. The gap in knowledge is akin to god vs. ants. I'll give you a chance to reincarnate only back 10-20 years (not 3.3m years like these characters), and you'd likely be the richest man on Earth by now, making the smartphone before Apple. Why would you think that modern human's imagination be limited to archaic weaponry such as bows, arrows and swords? Any modern human knows that gun is the great equalizer. You say they can't make intricate weapons, sure. So no revolver, no chain fed, magazine fed, double-action, automatic rifles then. But even a simple lever-action rifle like the Germans, hell, a matchlock, is enough to send all these cavemen with their insignificant human strength to death. Not to mention, we modern human know that the true WMD is bio-weapon. Brew some poison and suddenly a woman is every bit as capable a warrior as a man. Don't say that they can't, they've already created metallurgy.
I'm not suggesting monarchy or feudalism to be ideal systems of governance. I simply understand that Taiga is the one in a position of leadership. The people respond to him and his commands (because they respect him), and that's why his input would be necessary.
Who brought the concept of "king" to these people? Was it Taiga, or any person in the tribe? No, it's the Nazi German, who lived some 70 years ago, serving under their king-like Führer figure. And can you guess why these modern Japanese didn't immediately reject that idea being adopted into their new civ, even though they have enough capable men and women to form a small congress? Yes, because the author's propensity for a male absolute ruler. If this is just to appease the shounen demography, then sure, go ahead. But this is clearly a seinen series, so the fantasy fulfilling aspect of this decision is much harder to justify. It's more likely that the author is just inherently sexist, probably without even being aware of it. Again, patriarchal society's effect at play here.
Now, tell me, why do "people respond to him and his commands"? Why do they "respect him"? Was it because he's so much better at ruling, or his vast amount of knowledge unrivalled by any other of his group? No, because he fought like a cavemen amongst cavemen, so cavemen respected him. Are cavemen right? No, they're wrong. Their thoughts and ideals are primitive. It's not like the medieval and early modern eras when Europe sailed around to "enlighten lesser civilizations". This is actual cavemen we're talking about. Regardless, it only serves to further justify my opinion - the women are at the pivotal moment of changing their gender's image, position and strength in history, and since they're modern people, they, logically, should've been very, acutely, aware of it. The fact that they aren't aware and not fighting, is simply the author's oversight caused by being so used to living with patriarchal standards. He created uncompelling characters, plain and simple.
The women of his group can convene with him regarding organizing a social structure (and their place in it). Given his personality, I believe he would listen to them and move forward after thinking and discussion. Establishing a social order is quite a challenge.
Do you think having to convene, plead and justify your entire gender's power with a representative of another gender is something that looks normal? To even suggest such a thing...
Have we readers also regressed as well?
We also have to keep ethnocentrism in mind. Recall that a majority of people in their group have their own way of life. Altering that way of life can create conflict. Consequently, working with these people becomes essential. Do Taiga and his group have the right to impose their values and beliefs on the group if the group refuses those values/beliefs? I'm curious to get your opinion on the morality of imposing one's beliefs on other cultures if they are not receptive to it.
Remind me again who spread their culturally inappropriate Japanese language, way of thinking, mannerism, governing structure, technologies, clothing, etc. with these "ethnocentric" cavemen in the first place? Do they currently live in cavemen-invented brick houses©? Are they building cavemen-patented stone forts© and palisade walls©?
You're not dealing with cultured people from the bronze age, so your argument of "imposing one's belief's on other 'cultures' if they're not receptive to it" is very weak when the "culture" in discussion is of freshly appeared Homo sapiens, fighting for their hole-in-the-mountain with Neanderthals.