Government and critical thinkers in society have long recognized the traditional marriage as the NUMBER ONE!!!! institution, far more important than any others, that results in stable communities, good schools, public and shared resources, low crime rate/peace/security/prosperity/stability, and shared values that are constructive for all. A responsible mother and father in the home is 100% the very best recipe for children to become stable, confident, capable, successful, responsible and happy adults.
Double down on all that when communities of mostly stable traditional families are liberally sprinkled with churches and other places of worship. Religion contributes not only purpose and hope for people, but promotes conscience, charity, good will, people helping people through times of difficulty.
The fact that there are also good people in all categories outside the traditional family and/or whatever contrary anecdotes the naysayers will use to argue does not change the fact that without the traditional family, there is less opportunity for life, liberty and the pursuit of happiness.
Polygamy so blurs and complicates the lines of ownership, inheritance, lineage, etc. that there is nothing to justify it other than people want to do it. Most legal justification for banning polygamy is based on accepted societal standards for marriage and the public good. Polygamy is seen as lowering the status of women who become a harem governed by a patriarchal ruler who can disfavor one or more while favoring others.