Uhh... cost more? wtf? The actual act of enforcing capital punishment is relatively cost-less. Now the time, deliberation, and court costs to get to the decision is what costs money. And that's only because of the long and drawn out appeals process we currently have.
I am all for capital punishment. I do know that people have been in prison for decades that are now being found innocent after modern forensic science, ie DNA sampling, has proven them innocent. However, back in the day, more circumstantial evidence was all that was needed to prove guilt. With modern forensic science, and better accounting and culpability for investigators, that has dropped to near zero if not zero incidents. If memory serves me, in order to be convicted of a capital murder charge, there must be at the very minimum now DNA evidence.
The fact that modern science can prove 100% beyond a shadow of a doubt the guilt or innocence of a murderer means that we no longer need a long drawn out appeals processes so that the murderer can find some loophole to escape the full punishment of the law. If changed and instituted, then even this part of the process can bring down costs.
The last part of the costs of killing inmates being so high for most states, is once a capital sentence is handed out, most inmates sit on death row for YEARS, if not decades before being given their punishment. Not so long in Texas at least though. Anyhow, the moment a capital punishment is given, there really is no reason to wait. Just do it.
Finally, the last reason the cost to kill someone is high, is because of all the liberal hippies that complain it isn't "humane" enough. So we spend too much money on making sure the person dies as painlessly as possible. Bleh. A sharp axe, and a quick stroke are about as painless as it really is going to get. Sure it's a bit more gruesome, but to the person dying, it makes little difference. They are dead before the brain can register pain. The only reason we no longer do this is not for the person being killed, but for those hippies that complain that it isn't "humane." That and possibly the cleanup afterward.