The death penalty is justice how? By your logic of "justice", the thing someone does should be done to them. So a rapist should be raped. A thief should have something equivalent stolen from him. A child molester should have his child molested. I could keep going with this. This isn't emotional, its humane and sensible. I guess your opinion of the Iranian gov't chopping hands off for thievery is a given too right?
Your argument about people dying in prison is weak as well. A person that dies in prison is not executed by the gov't, plain and simple. Murders accounted for only 1.5% of deaths in prison in 2002. In that same year, the national murder rate was 5.6%. Its safer to be in a prison. Again, this is a moot point because your argument will always go back to the premise that they may die in prison so why not just kill them anyway.
Finally, if a person went to jail for something they didn't do, where do you think they would rather be? Death row or in general population on a life without parole sentence? If it was me, I'm going with life. Why? If I'm alive, I can still be proven innocent. If I'm on death row, I'm working with a finite amount of time, appeals, and chances. I'll take my chance with the way below national murder rate. On death row, if my chances run out, its 100% positive I'm dying.
United States Crime Rate
http://bjs.ojp.usdoj.gov/content/pub/pdf/shsplj.pdf