There is a fantastic podcast about public executions that I listened to years ago, which detailed how the public loved public executions no matter how violent or gruesome.
People would come from miles around, they would rent balconies above the execution site to get the best view and have parties while they watched someone suffer and die. Part of the reason public executions lasted as long as they did was governments being reluctant to take them away from the public.
I’m not sure that keeping it palatable is super important to the process. The real argument against execution is that we know for a fact that sometimes innocent people get convicted; to be ok with executing criminals you must be ok with the occasional innocent being killed, and I would argue that even a single innocent being killed by the state is too much to accept.