actually, I’ve heard of similar cases. If you want a second wife, often you don’t want quarrels so you ask your wife for help.
So why marry when you are not in love? I don’t know the Saudi culture, but in Africa, traditionally a man cannot have intercourse with his wife when she is pregnant or breast feeding and sex for women stopped at menopause... often a man would marry another wife, often her sister or relative so the wives wouldn’t quarrel.
In poor families, often a man would marry sisters or relatives so the wives could help each other in the work. And we had one man who married a wife every time he opened a store. Our African nurses explained why: You could have an easy job running the store (instead of working in the fields), you got plenty to eat, and a new dress every year.
Polygamy was one way to cope in the days when poverty meant starvation for single unmarried women.
It didn’t always work: Look at Jacob’s problems. And then there is the African proverb: Poor man, five wives, all pregnant...might as well be single.
Also, when men died in war, or went away in wars, leaving a lot of unmarriageable ladies, it also gave the unmarried girls a chance to marry.
The problem with polygamy is twofold: First, despite everything, women do get jealous.
Second: When there are almost equal numbers of men and women, often there is a woman shortage for wives for poorer men.
So like many customs that made sense in the past, they don’t have a justification in the modern world.
I'm going to think that many women like the system, for two reasons.
(1) If your choices are limited to sharing a rich man, or having a poor man all to yourself, many women will prefer sharing the rich man.
(2) Increased competition for desirable women means that most women will find a suitable man.