So what does a man get from polygamy that he couldn't have with fewer complications by phoning an escort service, or posting personals on the internet, or hanging out in bars?
Some men really do seem committed to each of their wives and all of their children. My father was like that. He was old-fashioned about sex, even though he was a doctor. He got embarrassed when sexual innuendos were thrown around even in mild fifties movies, and he had a hard time discussing the facts of life with his children. He said that sex was a glorious thing because it created life.
Some men are committed to having as much power as possible. And the more men and women and children you can control, the more power you seem to have—at least until everybody goes into rebellion.
If you want to know what motivates a polygamous patriarch to take several wives, look at the results. The Bible says, "by their fruits ye shall know them," which can be applied almost anywhere in life. In families where love prevails, you can be sure that at the head is a man in love with his wives and children, and they with one another. In families where it's all about staying in control, well…you can be sure that whoever heads that family has created a context where "my way or the highway" is the rule of the road.
Based on what you've seen of the FLDS community in Eldorado, Texas, what makes up the context of that religious group?