Some might find it redundant to sing the Kyrie immediately after Confession and Absolution. After all, we've already asked for God's mercy. That, however, is not the function of the Kyrie at this point in the service. As we now stand in God's presence, freed and absolved, we plead for the whole people of God, confident in the Lord's mercy to come to our defense.
In ancient times, as the king entered a city, the people greeted him with the words Kyrie eleison ("Lord, have mercy"). Their cry for mercy expressed their trust in the ruler to provide for their every need. As our Lord comes to us through his Word and Sacraments, we call on him to show mercy not only to us but also to the whole world.
The Kyrie is an excellent place where variety in the liturgy can be introduced. This is especially the case when one uses the bidding form (Ektene) of the Kyrie (e.g., "For the peace of the whole world ... let us pray to the Lord: Lord, have mercy"). There are countless Kyrie responses composed in all kinds of musical styles that can be sung by the congregation in response to a variety of bids. These bids can be general in nature, or they may employ a greater degree of specificity, such as praying specifically for people in all kinds of need. (It is probably best to reserve prayers for specific individuals for the Prayer of the Church.) While it is conceivable that the bids to the Kyrie could change weekly, it would be beneficial to repeat the bids for several weeks, corresponding perhaps to seasons in the church year, so that the congregation can become familiar with the prayers.
The Kyrie, as well as the Prayer of the Church, provides the congregation with excellent opportunities for intercessory prayer-an important task of the church that can be easily be overlooked.