I don't mind legalizing polygamy (though I disapprove of the practice), but would such legalization prevent an FLDS type of episode? Maybe the goals of the perpetrators are rape, abuse, and power-mad intimidation, rather than polygamy per se ("polygamy: merely a means to an end.") In that case polygamy legalization won't limit their ability to set up isolated, authoritarian, quasi-state cult compounds for their nefarious purposes.
Alternatively, if illicit polygamy is a marketing point that draws people to the compound in the first place, legalization may well help. Oddly legalization helps most when the religious belief (in polygamy) is relatively sincere and the abuse accumulates through evolutionary processes of increasingly bestial behavior; legalization helps least when the religious belief in polygamy is for cynical reasons of control and could easily be replaced by some other marketing point.
Is there entry into the market for polygamist cults? The FDLS and similar churches are no doubt attractive to a certain sort of man, but the leaders of cults generally want to suppress the supply of males competing with them. It seems to me that these cults largely increase by high birthrates, exit prevention for female members (via early impregnation), and forced exit for young males.
What little I know about cults indicates that male leaders do not advertise their sexual exploitation of female members. In the case of plural marriage, Joseph Smith didn't start practicing it until the mid-1830s, when his church already had several thousand members; other church leaders adopted the practice in the 1840s, when the group was more established and the membership numbered in the tens of thousands. The practice was not mentioned to the public until ten years after that. This would seem to indicate that the practice evolves in authoritarian, remote religious communities to which people are attracted for other reasons.
As I understand the history of the Mormon Church--though Will knows it much better than I--the Mormons were getting attacked by their neighbors and migrating to ever-more-remote locations long before said neighbors knew about the multiple wives. They didn't announce the practice publicly until after the trek. And they renounced it when they needed to be integrated into the rest of the country.
If polygamy were legal, the men in the FLDS still couldn't do what they wanted, which is to have sex with young girls. For that, you need mental control over the girls and their parents. I don't see the legality of the practice as reducing the incentives to act as the leadership did--they weren't hiding from the law, they were hiding from anyone who would tell women they had other options. Besides, from what I understand, polygamy is rarely the only weird and illegal practice that such cults engage in.
Like Tyler, I don't mind legalizing polygamy, though I'm pretty sure I'd never consider the practice personally. But I'm skeptical that this would prevent things like the FLDS's 13-year-old brides.
Update Incidentally, that post has the funniest comment I've read all week:
d.cous., if a society allows young men to study engineering, it does not care enough about 'disenfranchised young men' to warrant a ban on polygyny.
Of course, I immediately thought of this internet treasure: