King's desire to face the death penalty is basically an attitude of penitence for a crime committed. The issue of capital punishment is often misunderstood, especially in Christian circles. This was never meant to be carried out at an individual or group level, but at the level of the national or state government, and this was the level at which the ancient state of Israel carried it out. The state was seen as a symbolic representation of the rulership of God on earth. Much time is allotted before the actual carrying out of the punishment in a capital crime.
Time is and has been given for the accused to seek repentance.
Capital punishment is not meant as a way of cleaning out jails, but is meant as a deterrent to bad behavior. Also, it should be viewed by the state and society in a sobering and a saddening manner met with much brokenness by society in a world filled with much corruption. The state, then, should not see its responsibility in carrying out the punishment as a responsibility to society but to the One who ordains government, and this was the attitude of this nation's founding fathers. He, I believe, is a man who seeks to find peace in his soul. He is very much like the repentant thief on the cross.