This has pretty much always been my position, up until recently.
I think some people should just be put down like dogs; there's no reason to keep them alive just to be locked up in prison forever. Just take them out the back of the courthouse after conviction, and shoot them. Where there is incontrovertible evidence particularly, it shouldn't be an issue.
Will mistakes be made? Yes, of course (hopefully minimal). Will innocent people die? Probably (again, hopefully very few). But humans are not an endangered species, and innocent people die or are murdered all the time. Children die of cancer. Pregnant women die in car accidents. Good young men are murdered. I know someone who died simply because the health system was overloaded and his file was misplaced, so he didn't get seen for his symptoms for nearly 9 months - and by then it was too late for treatment to work and he died, only a few weeks after the birth of his first child.
The number of people wrongly executed would be a drop in the ocean compared to all those kinds of tragic accidents, or preventable deaths.
The only issue is that I don't trust governments to have that kind of power, and not use it for nefarious purposes. Although these days, I'm starting to wonder if it's worth the risk.
I see no benefit in keeping violent men alive, to potentially be released into society again.