Polygamy absolutely was prescribed, in very strong terms, in the form of levirate marriage:
If brethren dwell together, and one of them die, and have no child, the wife of the dead shall not be married abroad unto one not of his kin; her husband's brother shall go in unto her, and take her to him to wife, and perform the duty of a husband's brother unto her. Deuteronomy 25:5-6
And no, it is not universally portrayed as dysfunctional. Dysfunction appears when the subjects disregard specific instructions regarding marriage and sex, in the midst of polygamous relationships that are explicitly allowed by God. E.g., David's adultery, and Solomon's marriage to women from outside of Israel.
Um, yes it is. Levirate marriage is pretty simple; if a woman dies childless, her husband's brother is obligated to marry her so that she has a chance of bearing children, even if the brother is already married.
And for some entertaining context, go read the rest of Deuteronomy 25:5, where it says how the brother should be punished if he refuses the marriage.
> "Every instance of polygamy has a bad ending in the Bible."
This is simply not true. Tell me where Lamech's or Rehoboam's marriages caused a bad ending. And as I said above, King David -- perhaps the most famous of polygamists -- is never rebuked for his marriages. The Bible makes a very clear point of rebuking him only for his adultery:
David did what was right in the eyes of the Lord, and had not turned aside from anything that He commanded him all the days of his life, except in the matter of Uriah the Hittite. 1 Kings 15:5
That's a common misconception. It was described, but not prescribed. The polygamy in the Old Testament is universally portrayed as dysfunctional.