It is reductive and misleading to claim that monogamy is just a construct. It is far more than that. Societies have chosen to organise themselves around this idea because of the dangerous side effects polygyny can have.
As a report from the University of British Columbia found in 2012, "the intra-sexual competition that occurs causes greater levels of crime, violence, poverty and gender inequality than in societies that institutionalize and practice monogamous marriage." Societies without monogamy are therefore dangerous, unequal and poor.
This is not the only way in which the positives of monogamy outweigh drawbacks. As an organising principle it has many proven benefits across raising children, financial stability and mental health.
Given how societies develop, there is very little about them that exists in nature. This is hardly surprising.
More revealing is that scientific studies rarely point to the monogamy debate as the reason that people cheat. The case for marital norms driving infidelity is simply not strong enough.