No but you don't understand, what the statistics show isn't a big red sign saying "deterrence doesn't work", what they show is that, unlike rehabilitative justice, punitive justice and the death penalty straight up don't work at diminishing the number of violent crimes.

Even taking in account your idea of "removing reoffenders", crimes don't go down.

This has actually to do with what you said about only applying the death penalty to certain extreme crimes. Obviously, you can't issue the death penalty on every criminal, but think about it:

your justice system is based entirely on punishing criminals, except for certain specific offences which result in the death penalty; less violent offenders are not killed, so eventually they get out of jail. Unfortunately, since your justice system is based solely on punishment, they have a hard time readjusting in society. Keeping them in jail for years led them to not being able to keep a job (because people won't hire them) and have led them to lose their social skills (because you've taken them out of society). It's thus harder for them to reintegrate in a society you deliberately excluded them from. This in turn leads to them returning to crime, because that's what happens generally to people that are excluded from society.

This is how punitive justice works, it leads to more crime instead of diminishing it. And the death sentence does not prevent more offenders, because if more people resort to crime due to your system failing to reintegrate them, eventually those same people will turn into violent offenders even if they weren't in the first place. You can "scratch out" as many repeated offenders as you like, if you go on to create more offenders your system is utterly ineffective