I don't see any need for this. In reality, every child has two biological parents. To start complicating things with extra legal paperwork is silly and likely to result in unforseen downsides. Better to avoid government paperwork than to look at this as an opportunity.
It will only actually affect things in the event of divorce, and even then may if anything be less fair, as the biological mother's rights would be diluted, and whether that is just is highly debatable.
Gay people push for this sort of unnecessary and complex legal recognition simply since, for many of them, the state is effectively their god, the ultimate arbiter of truth. We don't need it.
I am not coming at this from a need standpoint as much as I am a utility standpoint. You can go back and see my posts in the past arguing that there are virtually zero reasons for government to be involved in marriage. I've advocated using contract laws and wills as opposed to marriage certificates. But, if a plural marriage can utilize the laws of the land in their favor, why not?
If given a choice between living in a vibrant democracy that provided freedom of religion as opposed to a totalitarian regime without religious protections, I would choose freedom of religion. Why? In an open society, I could utilize my time and efforts more effectively in evangelizing, or raising money to help others to evangelize. In a closed, unprotected system, a great amount of energy and resources are spent just keeping things underground.
Poly families could continue to choose to utilize contract laws, trusts, and wills, etc. but they would have to spend resources of time and money to set these things in order. If the laws began to recognize larger family units, then resources could be used for other purposes. It's a utilitarian issue.
In my U.S. state, the only document I need to make sure my wife receives all my assets in case of death is a marriage certificate. If we divorce, things are automatically split 50/50. Custody of children would need to be hashed out, but I would be guaranteed some form of custody or visitation unless proven to be delinquent. Beyond that, I need to set up a will or trust (which I have) to let the courts know what I would want to happen with my children should both my wife and I expire together. But I had to spend time and money to do that.
So, it's just a utility and resource issue that could reduce headaches for many poly families should they choose to go the route of the state.
There's a whole gigantic thread out there right now trying to hash out the law, sacrifice, Grace, etc. I don't see it as a "sin" to register a marriage, send kids to public schools, go to a registered church, worship on Sunday, etc. As children of Grace and leaders of our family, we need to choose things that do not offend our consciences, or violate scripture. But, we must be wise as serpents in seeking to support our families and protect them financially and physically. If the laws begin to change and recognize plural situations for protection of assets and care taking of children, why not utilize?
Okay, gut my answer. Can't wait to see the counter argument