Its not about sympathy, its about the fact that the death penalty achieves nothing.
It doesnt lower the crime rate (as proved by many studies over the years) and in many cases it would give "easy out" to these people. As PP's have said, many evil people have committed suicide as they didnt want to live out their days in prison as punishment for their crimes. And of course, again as PP's have pointed out, miscarriages of justice still happen. There is a huge question mark over the safety of Lucy Letby's conviction for example, the fat lady is a long way from singing on that one. Ruth Ellis was hanged 22 days after her conviction but evidence that came to light later showed that she was the victim of abuse at the hands of the man she killed.
As I posted above, the person who murdered my adults childs best friend was seeking their own death. Their actions against the best friend was in order to get that. So when the parents were offered the option to demand the death penalty (legal in the country that the crime and trial happened in) they refused. The punishment is the the murderer NOT getting the death penatly, which is what the murderer wanted.