Traditional polygamy for religious reasons involves man A and women B, C, D. One husband, multiple wives. The women can marry one man, the man can marry more than one woman, but the women cannot marry other men unless divorced or widowed. Less complicated than your above post.
I would support 1 legal spouse and decriminalizing polygamy if it weren’t for Social Security benefits, inheritance, retirement benefits, etc. At this point in time, a woman can be “spiritually married” to a man as a 2nd wife (for example) for 10 year and bear him children. If he dies unexpectedly, she has nothing but whatever he willed to her if he even had a will. The legal wife gets SS benefits for herself and any children, is entitled to his retirement, the house…everything. Ideally, she would continue to care for the other wives and children, but stuff happens. Jealousies, resentments, greed. 2nd wife could realistically end up destitute with young children.
Now, suppose he has a will with a somewhat equitable division of property and assets. Its well established precedent that wills can be overturned. A legal wife and legitimate children could still end up with everything. If polygamy were legal for religious sects, much like certain drugs are legal for religious sects, this wouldn’t be nearly such a problem.