If you're saying the first bit, you're saying that it's a disqualifier from the second.
Not to mention at least in the US the death penalty is more expensive than a lifelong prison sentence, so it's simply not a good idea.
It's an interesting story, but the historical record of how English law changed is, I think, a bit more interesting. Kids in London would steal. They'd go on trial. A jury of Londoners would see what looked like a twelve-year-old in the docket and just flat-out refuse to find them guilty because they couldn't sleep with themselves thinking they'd sent some kid to the gallows. This pattern became such an issue that merchants petitioned the King to pull back the penalties because as the system was implemented, it was going to stop protecting their property from thievery.
Liberal Europeans and Americans like to say that no civilized country executes criminals, but in fact several developed democratic countries in Asia do, and to say they aren't civilized seems absurd. Executing criminals seems to work well for them. Very curious.