And the priest shall set the woman before YHVH and unbind the hair of the woman's head and place in her hands the grain offering of remembrance, which is the grain offering of jealousy....
Numbers 5:18

The removal of the woman's headcovering in the Sotah trial represents the removal of her husband's authority and protection. He can't be both her protector and accuser. God, then, becomes her only judge and advocate.

It's hard to imagine that this procedure could improve anyone's marriage.