Wilkinson draws a rather useful parallel with drug prohibition: existing observations will necessarily be from the fringe and can't be used to extrapolate to a legal environment:
As a former tour-guide at Mormon historic sites, I have encountered more than one fundamentalist Mormon family in which the strutting husband seems to regard his flock of servile wives like glorified property. We're not wrong to want to discourage this. Moreover, those remote compounds in which exile fundamentalist communities brainwash their girls and discard their surplus boys are intolerable horrors. But this is all the more reason to bring polygamy out from the margins of our society. As with sex work, the horrors here have little to do with anything inherent in the practice and almost everything to do with the fact that we've made it illegal and dishonourable.I'll make a different argument.
The division of labour is limited by the extent of the market. We've tended to model families as being machines for home production. The family member with a comparative advantage in market labour does more of that for wages while the one with a comparative advantage in home production does more of that; more wages get earned and more home production gets undertaken.
Marriage has been shifting away from complementarity in production towards complementarity in consumption. Read Wolfers & Stephenson on this point. If a couple are both really good at market labour, they'll wind up outsourcing most of the home production. Nannies, maids, laundry services - all of these take the place of home production for high-ability couples.
Now suppose that individuals are heterogeneous both in abilities and in preferences over home production. Some high ability people simply really enjoy spending lots of time with the kids rather than spending lots of time out of the house. Suppose further that there are non-contractable elements in home production that get nicely sorted out via the implicit contracts in marriage. Marriage requires a whole lot of trust. Once you've sunk all the fixed search costs and decided that you trust someone enough to marry them, you can trust them on a lot of margins. Outsourced home production requires a whole new set of trust evaluations. You have to find a cleaner you can trust with your house. A nanny requires far more trust. Within marriage, love sorts out the non-contractable elements and encourages good outcomes. More marriage partners opens up more scope for the division of labour on household and market production: more people who can spend the day at home if a kid's sick, more people who can take turns covering during school holidays, smaller burdens imposed when one partner needs to head off for a conference. And, more opportunities for complementarity in consumption as well.
The law against polygamy isn't a binding constraint for us as I rather doubt we'd seek to expand were the law changed. But I'm not sure why it should be illegal for others to enjoy the advantages.