There wasn't polygyny in 19th, 18th and 17th century. Marriage worked with low divorce rate.
So it must be something else. You can start with no fault divorce.
Historically, King James instituted the 1604 English Bigamy Act. In this act, a man who was found to have more wives than one would be forcibly separated by sea for seven years. He had to be forced to choose only one, and the other wives would be pawned off to other men to marry. If he refused, he would be put to death and all wives pawned off to other men. It's evil.
Then there's Quanah Parker, an Comanche Indian, had 7 wives. He lived until 1911. He's one of the prominent polygynists in Indian culture. It was known that Quanah Parker had a visit from the Catholic Jesuits and was told that having more than one wife is a terrible sin in the eyes of God. Parker rejected the Jesuits and told them to get off his land. His wives stood by him and rejected the Jesuits too.
There was a wealthy British barrister, who turned into a preacher, named Martin Madan. He wrote in his three volumes of
Thelypthora: A Treatise on Female Ruin. He was a staunch proponent of polygyny, used the Bible as a good Berean, and quoted so much from the Bible through Hebrew and Greek. He espoused in these books that polygyny could help cure some societal ills such as preventing prostitution, ruination of women (like today where men can get laid with women and ditch them after they've "captured" their virginity), abuse of marriage and divorces where men could threaten wives that they could marry younger women. Charles Dickens is an example of this.
Believe it or not, polygyny has existed throughout the centuries, even after the Council of Trent. The problem is that the lineage of polygynists were not well known in the 17th, 18th, and 19th Century as there's no migration data or how many polygynists lived. Europe effectively ended polygyny around 1604 because the Catholic Church had such a stronghold over all nations including "divine right by popery". The popes would give kings "divine rights" to be kings provided they were the only kingmakers. As a result, they were able to keep tabs over kings. If any king got out of line, they were anathemized, excommunicated, and wars would result either in their deaths or a breakaway from the RCC.
Then there's Germany who lost so many men through World War I. There was a law back in the day around Munich, I believe, that instituted polygamy. Every German male available were to take two women and propagate. That's how Germany came back and started World War II because the populational loss of men in WWI was too severe. They had to rectify this.
Ethiopia has a long history of polygamy. It was recently in 1956 that they started a ban on it and are working toward outlawing it entirely. In African culture, every woman who has laid with a man sees that man as her husband. She can no longer have sex with another. I've seen a documentary on this where women cried over the fact they had sex with that man and could no longer carry on because they are taken. The prevalence of beliefs such as these is what makes Africa poorer. Men aren't considerate and too willful to sleep around. In fact, prostitution is the only thing African women have to turn to in order to make money, which further exacerbates the problem.
America was relatively untouched until much later on when Catholic Jesuits started roaming the lands, proselytizing their faith to other cultures. They also hunted down polygynists as well to force them to give their wives up. Polygyny did exist in 1900s and onwards. The formation of Mormonism, Joseph Smith, and other religions sprouted up as a means to acquire illegal gains without biblical application of the true Bible.
Marriage did not work a lot under monogamy. Nero executed Poppeia, and his other wives as a serial monogamist, married a boy who was neutered and turned into a woman. He was raped. Then Nero burned Christians on the cross at night, relishing in their screams and the light illuminating Rome. The accounts given around the fall of Rome showed that decadence, corruption, and sexual impurity were being carried out. Prostitution, engaging in sexual acts, even inside the temples and whorehouses, were seen as a rite of passage for young men and the elders would encourage the continuation of slavery. The Praetorian Guard fell to their deaths due to skullthuggery and were slain. There were other evil emperors too at the time who did abuse their wives. Then there's King Henry of England (I forget which number) who would marry multiple women including Anne Boleyn then had her executed.
In Madan's three volumes, he also outlined what happened in Victorian England. The men were drunkards, serial monogamists, wife abusers, rapists of women. He even pointed out that they also chased after children. And there's a whole slew of how the men would abuse the law of God through their manmade laws by enjoying marrying one wife, divorcing her, then marrying another without biblical grounds for it. The way Madan wrote it, it's similar to our time only that each century is dressed up in a different way with the same methods being applied throughout all centuries.
No fault divorce may have contributed to the rise of divorces through non-biblical grounds but it is not the defining factor. The problem is that despite Madan's records and testimony of what happens in Victorian England, you will always see the same things being done in each century. I am sure that in Victorian England, they had no laws about no fault divorces. I am not 100% confident on that but I am sure that they did not. Do you know why?
Our laws in the U.S. are modeled after English Common Law. The laws of bigamy only sprouted up when Republicans back in the day called for the end of the twin relic of barbarism: slavery and polygyny. Slavery still exists today but let's not get ahead of ourselves. Polygyny is still thriving, but not in mass numbers. However, we do have anti-bigamy laws that existed in recent times, which suggests that since 1604, that mere measure being instituted by King James, England was already working toward that ban. America only followed after in 1856 when the Republicans called for that ban. That's 252 years in-between.
I've said it before. Common Law in the US derives from English Common Laws. All English Common Laws derive from Catholic laws. All Catholic laws derive from Rome, who instituted their principles and formation of laws. As the quote goes, "All roads lead to Rome." In this case, "All laws lead to Rome."