Jason Engwer has discussed polygamy on exegetical and theological grounds.
I'd like to approach the topic from a different angle.
1) There's a basic distinction between showing and telling:
You can use words to explicitly render a judgment on an action. The use of direct speech or writing typically fills this role.
Or you can render a judgment implicitly. There's the obvious case of body language. For example, if you assert that your wife is looking a little larger around the midsection, her facial expression will communicate a clear, non-verbal (as it were) message.
Film is a medium that regularly utilizes implicit language. All of us have watched documentaries wherein no overt judgments of speech are made, yet stock framing techniques tell us exactly what or who to approve or disapprove of.
Or consider the political attack ad. Sometimes these ads simply state bare facts with photographs of opposing candidates. The candidate you are supposed to support is featured in pleasant or dignified color shots. The other is portrayed through awkward or menacing grey photographs. Sometimes soothing or jarring music accompanies the montage. Without any direct speech, the viewer knows exactly who should be supported.
2) These modes appeal to standard narrative techniques known to the audience. They in turn assume a certain moral framework, a feature common to all literature.
For example, we want Darcy to marry Elizabeth. The narrative of Pride and Prejudice assumes we value marriage and believe the happiness of Darcy and Elizabeth to be a desirable end. The novel would fail if we lived in a society that thought marriage was a grave evil.
Characterization and representation also play roles here, for even though we are never told to despise Mr. Collins, the reader inevitably judges him a man of dubious quality, an obsequious buffoon.
It also paints a negative picture of the institution of the church as well, inasmuch as gentlemen would select the church as one of a few career paths as a means to obtain wealth and prestige, rather than serving God as an end in itself. Mr. Collins, as it were, serves to characterize the whole of the church of England.
Detective stories operate under similar moral assumptions. We assume that solving crimes is of value, and that apprehending the perpetrators is a worthwhile pursuit. If the detective is morally deficient, it clashes with our moral expectation, as occurs when watching American Gangster.
These stories generally don't tell us what we should think through direct speech, even in those cases where they are criticizing a prevailing norm. Indeed, some of the best literature paints rather than lectures, the narrative voice leaving a moral "impression" rather than a statement.
3) When it comes to polygamy, some people think Scripture has nothing to say on the subject, or tacitly approves of the practice, because it renders no overt, explicit verbal condemnation.
Yet that expectation has more to do with a general failure to appreciate literary forms. Here Evangelicals fail as often as wooden atheists, for not everything important in Scripture is explicitly stated in theological propositions. Didactic knowledge can be related by example or implicit literary techniques.
4) The Bible, in a particular sense, is literature. So a literary lens can be a useful perspective from which to analyze the Scriptures. It also has the benefit of dodging debates over historical criticism, for it treats the Bible as a unified whole.
As I understand it, the Bible uses stock ANE literary techniques.
It also builds from an assumed moral framework, drawn from the surrounding culture.
Polygamy, while practiced among some of the elite, was still rare in the upper classes, and all but absent from the peasantry. And from what we know of the relevant ANE case law, it was usually only acceptable as a means to remedy infertility. Even then, it was generally regarded as improper; monogamy was the ideal.
So we need to keep that in mind when reading stories of polygamy in the Old Testament.
5) Consider the characterization of the line of the serpent in Genesis 4, which is deliberately contrasted with the Godly line of Seth. Lamech is the seventh, and thus archetypical, representative of the line. He is nothing more than a thug, though nothing less than a highly dangerous one.
The reticent nature of Biblical narrative is yet again instructive, for the mention of Lamech's bigamy, the first of the Bible, is hardly some passing historical anecdote. Rather, the narrator is instructing us to see the characteristics of the ungodly against that of the righteous, while retaining the backdrop of the Garden of Eden. It is the line of Satan that takes more than one wife.
Good social criticism does not merely denounce a position, but draws us back to a better standard. The narrative of the Pentateuch and the Old Testament is framed around the Edenic standard of Adam and Eve. Every story of marriage has in its background the now-lost bliss of monogamy.
6) And so polygamy is always characterized in a negative light. Whenever its details are revealed, it is shown to inflict enormous social harm. Even when it produces more children, the attendant bitterness is all but overwhelming.