Yes if we are certain we have the right killer.
How are we ever certain unless he does it in the middle of a crowd and then sits on the body unmoving until the police arrive? Digital evidence is getting easier and easier to fabricate, right? To those that think life in prison is almost equally unjust...who knows what technology like DNA will come along? If the alleged killer admits it, do we know it wasn't forced? What if an innocent man would rather be killed than spend life being raped by the other inmatess? And we still have an adversarial justice system that essentially rewards overzealous prosecutors and indeed prosecutor misconduct.
I think the biggest problem for us anti-death penalty people is that oftentimes the most obviously weak cases against the condemned are supplemented by the accused being a genuinely bad person. Wife-beaters, people accused of past crimes, etc. are all more likely to end up in jail falsely than your prototypical rich suburban types....
Lunar, some murders I think we know beyond per adventure who the killer is. Consider that guy who blew away a bunch of folks from a tower at some university in Houston about 15 years ago. Some kills are on tape. Others have DNA evidence. I suspect that we know to a moral certainly who the killer is in a majority of death penalty cases. Sure we know nothing for certain, or so the philosophers tell us, but if the odds get high enough to reach a moral even if not absolute certainty that is good enough for me - say where a life is at stake a million to one, or something along those lines.
Sure a lot of murders are prosecuted on thin evidence for often execrable ulterior motives. As I say, nobody gets sentenced to death without a higher court making a moral certainty finding. That is my opinion.