Speaking from a Lutheran perspective…
I wish it were more commonly practiced. It can be a very powerful and comforting thing and should be common place. It is comforting to hear a priest/pastor pronounce God’s forgiveness to you personally. I also think it is a great cause for sinners to reflect on their sin and strengthen their faith to avoid further sin. Unfortunately, it is rarely done among Lutherans today.
Lutheran doctrine does not oppose private confession (penitent to confessor). In fact, quite the opposite. Luther himself wrote frequently on private confession, stating in one of his writings… “I will let no one take away private confession and would not exchange it for all the wealth of the world, for I know what strength and comfort it has given me.” Philip Melancthon wrote in “Loci”… “Private absolution is thus as necessary as baptism.” And the Lutheran Confessions repeatedly address the benefits and necessity of private confession and absolution. In Luther’s Small Catechism he actually provides the format of a private confesstion and how one should confess.
So, as for private confession itself, Lutherans (officially) and Roman Catholics are quite similar. Where I think Lutherans (those who hold to the original Lutheran teachings) and Roman Catholics will disagree, is on the penance (I hope I’m using the term properly). The Roman Catholic priest will decide upon an appropriate response for the confessed sin (i.e. one Our Father, etc.). The Lutheran sees sin as already being completely paid for by Christ’s sacrifice on the cross, the pastor will pronounce God’s forgiveness, but there will not be any further “to-do’s” to make amends for the sin.
As to why private confession is so clearly proclaimed in Lutheran doctrine, yet not commonly practiced… I can’t say for certain. Unfortunately, over the many years since Luther, there has been a tendancy to cease many things that people perceived to be “too Catholic.” I suspect private confession fell to that same mentality. Other similar practices would be making the sign of the cross, the prominence of the crucifix (opting instead for the “unadorned” or bare cross), kneeling for prayer, etc. I’m happy to be from a pretty conservative/traditional Lutheran heritage that keeps much of that.
Hope that answers your question.