Having multiple wives was permitted in the Bible for the same reason disobeying God is. God honors man's free will.
Had God intended that man should have multiple wives, why would he only create one for Adam. Most assuredly since God wanted man to multiply and fill the Land having multiple wives would enhance that program exponentially.
Genesis 2:18 And the LORD God said, It is not good that the man should be alone; I will make him an help meet for him.
Genesis 2:21 and 22 And the LORD God caused a deep sleep to fall upon Adam, and he slept: and he took one of his ribs, and closed up the flesh instead thereof; And the rib, which the LORD God had taken from man, made he a woman, and brought her unto the man.
Genesis 1:28 And God blessed them, and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth.
Those Scriptures are not there to tell us what God allows, but to teach us the progression of man's defiance of the rule of God, and the need for extraordinary measure to bring mankind back into God's grace.