When a soldier, sailor, airman, or marine in active service commits a crime, he or she is tried under the UCMJ. The military has prisons, and the military has a death penalty for certain crimes. So far, military law is just like civilian law.
But there's one major exception: any penalty given under the UCMJ must be signed off on by the convicted person's commanding officer. In the case of the death penalty, that extends all the way up to the Commander-in-Chief. Yep, the President must personally order the execution to be carried out, or the fellow winds up cooling his heels on death row indefinitely.
The last President to authorize execution of a capital sentence was John F. Kennedy. In the meantime, military death row has filled up in the normal course of things. But nobody is ever executed, probably because no President since Kennedy wants to have to order it done. Squeamish? Wary of bad press? Who knows?
But you see the difference, I hope. Under civilian law, the Governor or President has the option of extending clemency, but can choose not to, and things will simply proceed to the conclusion ordered by the courts. Oh, the Governor's signature may be required on the death warrant, but he can't just put it off without defying the courts: the only real option he has to carrying out the sentence is to grant clemency -- and face the gaff for that. It's easier to just let it roll by. But without the Commander-in-Chief's signature, the prisoner is in limbo, and just rots on death row.
So, which is better? If every Governor had to actively decide to carry out an execution (with the option of leaving the guy to cool his heels for the rest of his life), would that mean fewer executions? Would that be more just? Or if the President didn't have to order an execution, would the backlog on military death row be cleared out, and would that be more just?
And would making every Governor have to choose to carry out an execution unbalance the separation of powers by diminishing the authority of the judiciary? This doesn't apply to the Armed Forces, since they have their own courts, which function under the authority of the Commander-in-Chief. Both Congress's role in creating the rules under which the military operates and the President's responsibility as Commander-in-Chief are specified in the Constitution. This is also why the President has the power to create military commissions and the whole judicial process for them, if need arises. In effect, the ordinary judiciary is held at arm's length because people in uniform are in a special relationship to the government that the free citizen is not. So, would making Governors have to confirm judicial sentences place the free citizens of a State in a lesser position vis-a-vis their governments?