She has all reason to be careful. Because in a way Yuri is quite close to being the ideal woman. She's not physically imposing like Miku or radiating Yandere vibes like Hinata. In a way she's competing with Kana herself, having a small frame and Yuri is actually plenty cute, so she's less likely to induce fear in men. Especially so because until now she did not express being into males that much, if at all. She's not exuding lust like other girls in the class. Not to mention, Yuri is not failing in terms of her grades either, being rank #8 might not be at the top, but it's still in the upper part of the class. Tthe key point is that Yuri was disappointed by the guys she met and she probably stopped putting in her utmost effort after entering the academy. And yet, Yuri still achieved her rank. Just now she showed her "Dark Horse" power. Or rather, she demonstrated resilience of a level where even the actual three guards could hold their ground. It also left a positive impression on Sou's family - from Kanaria's point of view that's more than the guards achieved so far. So it's not hard to imagine what might happen if such a girl would actually meant business and took her training as a guard seriously. Yuri stated herself: "I'm a woman who can deliver"... and right now she demonstrated that she can. Now add the fact that she did not actively pursue Sou, but Sou went to her instead. Objectively speaking, Kana's worries are more than justified.
"She is not exuding lust like the other girls in the class"
Sumire-nee would highly disagree given she put Yuri into the same category as Miku in terms of lust.
I would say, rather being being "the ideal woman", Yuri is closer to being "a regular woman from Satou's world" in the way she treats him. Like none of the other girls dared to speak to Satou and when he did they overreacted in ways that made him second-guess himself. Yuri on the other hand was proactive with her letter. She could look him into the eye and be with him in a toilet room without losing her mind. And while she behaved like a brat who hated him, her indifference to him (save for Miku lusting after Satou) was probably closer to what Satou experienced in his world he came from.
That he wasn't special.
As for her rank in class we do not know how that scale school wide as we have not been given her school rank. It probably could be anything between 14 and 100 at this point. But yeah, she sure showed off what a strong woman she is with how she survived Satou's "rejection", even if it cost her her iron virginity.
I just have the feeling Satou will end up with a single girl/woman, despite the world's norm clearly being having multiple wives, because of how he thought to himself "maybe I will even get a girlfriend" when first coming to school. "A" girlfriend. One. Not several, not multiple, not a harem, just one regular girlfriend.
In his eyes thats probably the best he can hope for, in this world's eyes though? He must seem insane.
Either Natsuki or Yuri got so far the best chances for that position, and I would favor Yuri because Natsuki ain't truthful, neither to herself, nor the others or even Satou himself. I don't like that. I get why she does it, based on her own experiences and values, but for a deep loving relationship? Not a good start.
And while Yuri is a mesugaki and a tsundere, she is honest with her feelings (except for wanting to mate with Satou), reliable and always comes through with Satou.
But most importantly:
She said "good morning" normally when he greeted her.
I think that left the biggest impact. How his "good morning" was just responded to in a usual way as it would be in Satou's world.
They would be treated like unicorns, Santa Clause or be on par with urban legends.
I'm afraid they might be treated like polygamy couples would be in our world. As abnormal. Whatever that entails.
I do agree, that single mothers are the norm. Virgin single mothers are the vast majority, followed by co-wives then by the actual first wives whatever that kind of life-style means.
We do know that women and men see women as "lustful sows", "dangerous sex pests" and "ladies". There seems to be a hierarchy based on education/behavior that makes it more likely to become a wive of whatever rank than just a semen receiver. Like even Kanaria's big sister is without a man and it seems their family name is a real big-shot name, like with influence, money and power.
And the way Natsuki's mother behaved in her memory, it seems being a co-wive ain't quite the happy life either.
The way everyone reacts so strongly to scent makes me also think that their noses must be much finer and stronger than our world's noses since Satou is oblivious to the "stank" of lusty women or his own "sweet scent".
We know Satou's current family is already considered out of the norm due having Sakura. As Suzuki demonstrates, the norm is to get a boy aka jackpot and keep that boy in the family, protected by mother and sister. And given Sumire's thoughts about older sisters and younger brothers, incest does seem to be not unheard of. Probably the reason why for each child the mother is given different sperm to create half-siblings rather than full siblings. Though I am not sure that helps that much.
We know 33 year old men get raped by 16 year old school girls after getting drugged, we know about kidnapping, we know about most males suffering under their restricted freedom to leave home like Erika's guard memory has shown with her guard target. We know males are often gay when getting to male only schools and that a lot of males are afraid and see women mostly as beasts or servants.
But our main story Satou is so out of the norm for this 1:39 world I just can't see him getting a harem or even wanting one. Because in his thought he couldn't treat them all right and that would depress him to no end with how kind he is. I can see him opening a "Positive reinforcement Agency" where he basically does his ritual of telling women their good points and praising them. I could see that being a huge hit in this world given how Sakura and everyone who received his praise so far reacted to it.^^
But yeah, we don't know if 1:1 families exist in this world or not. Seems highly unlikely. If they do I believe the woman in such a relationship must face both mass envy as well as mad respect from other women. I guess as long as the husband fulfill his semen deal to society, they can be in whatever relationship they want.
Government probably is even fine with gay couple as long as they provide semen regularly than compared to a guy who father 5 children with 3 different women but doesn't come for whatever reason to do his monthly donation.
And then there is Satou with the weekly visit. For mankind ofc. XD