There will be miscarriages of justice. So you will be executing some innocent people. Maybe not this guy, but once you bring it back it’s an absolute certainty that some cases will be wrongly decided.
Also someone had to be the executioner. I don’t think we should be in the business of either putting someone in that position or encouraging anyone who is happy to do it.
Also it’s very much arguable that a whole life term is a worse punishment - but doesn’t fall foul of the above difficulties. Anyone wrongly convicted can be released when it comes to light, but they can’t if you have killed them.