"I'm torn between my more general feelings about capital punishment and the part of me that asks why something like that should be kept alive."
Why?

1) Because of what it says to our children. Here is a problem you can solve without descending to killing to someone. Adolf Hitler - you have to kill people. Richard Speck - you don't.
If you practice violence in this case - you are doing it from personal preference, rather than necessity.

2)Our society is churning out more and more of these social inadequates - we need to know why. Focus on the problem, rather than some medieval bollocks about good and evil.

3) Sadism - the desire to voyeuristically enjoy cruelty is deep within all of us.
True Crime Porn and public enjoyment of the execution - who hasn't turned to the gory details of Charles the 1st on the scaffold and poor Mary Queen of Scots, and a myriad others and enjoyed the grisly details?
It is a base strand inside the human make up - every manifestation of it should be resisted for the sake of human dignity.

4) I'm not up for it.....