Only if there isn't even an unreasonable doubt that the person is guilty. Which pretty much leaves you with the people who confess, who are usually going to have a plea bargain anyway.

Just because someone confesses doesn't always mean they actually really did it. Maybe they were threatened into confessing, maybe they lied for whatever reason (most probably because of psychological problems), maybe the police questioned them for hours and they just wanted it to be over. There are a lot of reasons why people would confess to something they didn't actually do. A confession is not fail-safe, just like the whole justice system is not fail-safe.

Only when there are no mitigating factors. Such as, under the influence of drugs or an untreated mental illness.

How many people would that actually leave us with? I mean, the death penalty would only be for serial killers and mass murderers, but also only for those without a mental illness or those on drugs...who would be left? Because I don't think there are that many serial killers/mass murderers who can be counted as "normal".

Needless to say, I don't think the death penalty is a suitable way of justice in any case.