I'll quibble.
In Asuran society, men have zero intrinsic value.
They're not needed for reproduction, they're not needed for social interaction/marriage, and they've already been mostly eliminated from the work force.
Asuran females prefer to have daughters, leading to a consistent massive gender imbalance for centuries. Their society has successfully adapted to male-less-ness.
Men offer absolutely nothing, and they couldn't even if they wanted to.
Why would Asuran women even bother with them? This is not explained.
The Mormon example:
Sons would not be in demand. They would be in negative demand since Asurans prefer to bear daughters. Sons would have zero social value.
Daughters are in high demand, as mentioned. Daughters have high social value, because they are full members of society. They have bear children and they participate in the economy.
Mothers and daughters wouldn't compete over men, because men aren't needed for anything. If a woman swings that way, and I said if, she'll only be competing with women who want a man's company. It will probably come down to who can make it worth the man's time. But, he will be a luxury, a toy, a kept man. So, I agree the best of men will be with the rich or powerful women, regardless of the women's personal qualities. There's nothing to stop a man from being with a woman he likes, but if he wants a comfortable life, he needs to go for established women who have resources.
I don't see how marriage would exist in Asuran society at all anymore, but if the op says it's in there, it's in there.
I don't think men would be needed as breeding stock either, since with Asura's TL they could combine DNA from two female partners. Given women's penchant for list making when it comes to partners, most men would be eliminated anyway (well, he needs to be over 6 feet tall, handsome, very intelligent, sensitive, happy, with a talent for art, with good eyesight, perfect teeth, this color eyes, no negative genetic predispositions, etcetera ad nauseam, ad infinitum). From tindr research, women reject 80% of men on looks alone. Add genetic analysis to that, are hardly any men will qualify. Let's see, men are about 25% of the Asuran population, and 80% of them will be eliminated on looks alone. Not looking good.
IMO crime would be very different. There would be much less physical violence and far more social violence. Ostracism, workplace mobbing, emotional abuse, all the female social hierarchy games would go completely unchecked. Social competition at work would be intense, and since they're all women HR isn't going to swoop in and save anybody's bacon. Police aren't going to respond over people's hurt feelings, even if it's a rampant social ill. People wouldn't know any other way. Depression, self-hate, and suicide would rise. Young women entering a new workplace would probably be demeaned while being forced to smile and take it.
That could be a reason some Asuran females still take up with men: men want them and value them, just because they're women. With a man, women can relax and be loved. But, taking up with a man could be jumped on as a sign of weakness by other women. Mockery and ostracism could await any women who is discovered.
Unmarried men wouldn't cause crime because anyone who stepped out of line would most likely be shot or imprisoned quickly. The police would investigate, the victim would say "I don't know it was some man," and the police would round up all the men and torture them until they found the perp. Then the politicians would enact polices to control men. Implanted RFID tags, special co-ed neighborhoods which men need a pass to leave, or just isolated labor camps where men can live out their useless lives doing factory work or resource extraction to pay back women who are so generous and kind to provide a nice factory for them to work in and a nice bunkhouse for them to live in. All that electrified barbed wire doesn't pay for itself you know, and casserole isn't free. Also, the brainwashing would be extreme. Your poor self-sacrificing mother wanted a child so much, but you robbed her of the daughter she wanted, because you're a boy! It's the least you could do to learn to cook a good casserole!
Off Topic:
I would appreciate it if anybody would look over the story I wrote in the library section and leave some comments so I could improve. 700 views and not one comment.
http://www.travellerrpg.com/CotI/Discuss/showthread.php?t=38719