I see nothing productive about that.
Nothing productive? Instead of taking two people out of the population, you take one, and replace one useless being with a human who is willing to work and sees their errors. Is that not a greater justice? If you died would you rather have your death destroy another, or have that person reenter society and do good?
Executing minors is a whole different story. A 17 year old shouldnt get off after killing a few people just because he is legally a minor. I think you will find that very few if any young children who could not think on their own have been executed. Remember its up to a jury or judge, so just because there isnt a specific law banning minor executions doesnt mean that every child that kills someone is executed. Im happy with the law as it is in that case because of the example i cited above. There are many 16/17 year olds who act just as adults and deserve to be treated that way.
I can point you to a number of studies that will tell you that during teenage years the brain is undergoing a growth spurt on the level that a three year old goes through. During this time teenagers don't have alot of self control, infact a pre-pubescant probably is able to act more rationaly than a 15-16-17 year old.