Okay, now that I'm done teasing franz and Gale (though, I still think they might make a cute couple...I'll leave that to them to pursue), I'll address the actual topic.
The primary rationale that was put forward for polygamy seemed to be to alleviate the burden of parental responsibilities on those who need to work by more of a communal living arrangement where the women (he didn't mention the men in this) would sort of have rotating shifts of childcare responsibility for all the children and then could work the rest of the time.
As Astronuc pointed out, the likely conflicts that would arise in the marriage(s) would probably far outweigh any benefit, and it seems if the objective is to take away the burden of finding daycare, there are better ways to go about it.
There's an idea I've had that I've mentioned to others in a joking way, but has some potential to be practical, at least for some workplaces. There seem to be about three major problems I see arising as parents put kids into daycare to return to work.
1) Daycare has only limited hours. All the parents need to leave the office no later than 5:30 PM to pick up their kids by 6 PM. This leaves them very inflexible to stay for an important meeting that needs to be scheduled near the end of the usual work day (it's not uncommon to have a 6 PM meeting for something urgent because it avoids the conflicts of everyone's already fully busy days), and even if they are in the middle of something that would be better completed in one sitting without interruption, they have to drop it and go get the kids. And, if the daycare is closed for a day (school holiday but not a work holiday), the parents need to take a day off from work to stay with their kids.
2) The kids don't see their parents during most of their waking/playing hours when most people agree it would really be good for the parents and kids to interact.
3) It only takes one parent to drop the kid off or pick the kid up at daycare, and it seems there is still a heavy bias toward this being the job of the mother, so all the disadvantages of needing to cut the work day short seem to weigh more on mothers than fathers.
So, what do I propose? Parent-run daycare/babysitting in the workplace. Rather than charging parents for enrolling kids in daycare (a small fee may still be needed to cover supplies and facility upkeep), you have them rotate turns babysitting. And, you include both mothers and fathers to take the burden off just the mothers.
Somehow, I just think it would be more cost-effective to have parents responsible for a half day a week watching kids (of course, for this to work, you'll need a certain critical mass of parents and kids, and it might work best in a medium-sized company than a very small or very large one), when you can schedule for them to be away from their desk, but they are still in the building if you need to ask them an urgent question.
Their kids are nearby, so they can stop into visit to check how things are going or just to get a hug, and are guaranteed to see them a half day every week. If it is common for people to need to work late, you can set up the daycare hours to be more consistent with workday hours, plus, even if they have to pick up the kids at a certain time, there's no travel to get there, so you save at least a half hour a day of travel time, which already makes up for the half day of unproductive time taking a shift watching kids. You may need to supplement the daycare staff with some full-time day care workers, but won't need to hire as many if you have parents helping out too.
Plus, it would foster more of a reciprocal relationship among the parents where it might be easier or more likely that when one parent found themselves in a pinch needed to stay late for a meeting at the last minute, they could call upon one of the other parents they work with to watch the kid for an extra hour, and then return the favor at a later time. This is a lot easier to do if the kid is right there and not off at some other daycare location. It's not so easy to just ask a friend to go pick up your kid at daycare if you can't make it in time, because the daycare won't give the kid to just anyone (rightly so) and they won't have the carseats or booster seats needed since they need to drive the kid somewhere else.
This would probably be even more popular in a place where you had a substantial number of night shift workers, when daycare is generally unavailable and full-time babysitters hard to come by. You could have a place for younger kids to sleep and older kids to get their homework done or play games when they are done with their homework. There are people who need jobs and would take those shifts if they had a place where they thought their kids would be safe during that time.
Is this overly idealistic to think it might work?
I just read this in a dutch newspaper and thought it's hilarious.. is this guy serious?
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Yeah, that doesn't sound like a very good plan to me. I prefer it as initially presented...it would give those of us who are sure all the good men are already married or taken another chance at them! 
I would not be a good candidate for caring for someone else's kids. Do you remember my posts about that little boy I nicknamed Vermin? 
