I can’t really address the argument for ‘nature’. It may well be that the arguments from ‘nature’ do exclude polygamy.

I can address the argument from tradition. At least as I understand it, arguments from tradition presuppose that cultures and traditions have a sort of deep logic built into them that make big changes to fundamental institutions very unwise and destructive of the good. In the Burkean iteration, tradition is also a window to ‘nature,’ in that the collective wisdom of age long experience tells us deep truths about the human condition that we can’t access by our own reason and argument alone. These arguments are just presumptions, however. God can trump tradition because God knows the deep truths of the human condition with certainty. So in 1830 a Mormon can argue against gay marriage and polygamy and children being raised by their own parents and so on because of tradition. After 1850, a Mormon like me who doesn’t believe in excluding religious arguments from public discussion could say that revelation has excepted polygamy from the lessons that tradition teaches, and then point to the existence of polygamy in other societies and in the Biblical roots of our own tradition as some justification.