Multiple wives were never explicitly permitted by God. When he created marriage, it was to be between a single man and woman for life so that mankind couple multiply and fill the earth and so that he could model the relationship between Christ and the Church (Ephesians 5). The first person mentioned in the Bible to take it upon himself to have multiple wives is Lamech from the line of Cain, the same man who boasts in his violence.
The thing that makes polygamy difficult biblically is that there were so many opportunities to rebuke people for taking multiple wives, but God didn't do it, despite still rebuking them for other reasons, including sexual reasons. Even when David takes Bathsheba, he is rebuked primarily on the grounds of his theft and murder from Uriah rather than the sexual deviancy of voyeurism, lust, and compulsory sex. We can still understand that David's sin was sexual by doing good systematic theology, but it seems odd that God would not rebuke any of the patriarchs for polygamy.
The internal logic of polygamous marriage at the time was to generate heirs. If you are limited to the offspring you can produce with a single wife, you have a 5-10 kid upper limit. For each extra wife, you can expand just that much faster. In tribal structured government, and when dealing with ruling dynasties this is a big deal.
Israel should have had faith that God would provide them with the heirs they needed and that he had promised without going beyond the boundaries that God set for marriage.
Nevertheless, this appears to be one of those issues that God made an accommodation for something that he still considered sinful, just like the issue of divorce. Jesus called divorce sinful, Moses merely required a certificate of divorce. The Mosaic regulation was still from God, but it merely mitigated the damage of divorce since divorce proceeded from the hardness of their hearts. In the New Covenant, Christians are given a heart of flesh, which means that we are not subject to the law of God as a Covenant of Works but as the Law of Christ. Therefore, while the ritualistic and cleanliness laws have become obsolete, the moral law has become more exacting. The hardness of heart is no longer a valid excuse for merely putting limits on sinful behaviors like divorce.
Likewise, my conclusion is that polygamous marriage is something that God overlooked for a season despite being contrary to his design, but for Christians, it must be abstained from. This also can give us instructions on how to respond to situations of polygamous marriage in the mission field. They can be considered true marriages that should not be broken apart in order to satisfy repentance, but marriages that should not be repeated and perpetuated any longer. Contrast this with illicit marriages like homosexual marriages which should, in fact, be broken apart to satisfy repentance.
