I don't think it tracks that finding this horrific is indicative of sympathy for the perpetrators. Believing that a civilised society doesn't kill its citizens, let alone live stream executions for the edification of the masses, doesn't mean your sympathies are with perpetrators of crimes rather than victims. It just means you think there are depths to which governments shouldn't sink.
I also think these executions result in far more attention and sympathy being directed at perpetrators of crimes than a life sentence would. Look at the Christa Pike example - what she did to Colleen Slemmer was unspeakably evil. And had she been sentenced to life in prison, she would have faded into miserable obscurity like she deserved. But instead, she has become an object of public empathy because her botched execution was so horrific that people are naturally revolted by it. And instead of the focus being on Colleen, who deserves to be remembered with grace, there is a raging debate over whether her murderer is being mistreated. It's an absolute fiasco which does no justice to Colleen's memory.