Would these kinds of curses be more effective at curbing crime than prison or execution?
There are four goals of punishment:
- Incapacitation. Prevent the criminals from committing other crimes.
- Retribution. Punish so that the victims don't have to do so.
- Deterrence. Scare potential offenders from committing crimes.
- Rehabilitation. Give the criminal skills to gain employment, etc.
Curses may be more effective on retribution and deterrence, but they are utterly ineffective on incapacitation and rehabilitation.
Punishment type doesn't deter
The truth is that even mild punishments deter if coupled with removing any gains if they are always applied when deserved. There is very little reason to believe that stronger punishments deter more. More consistent convictions are more important.
The issue is that most people don't expect to get caught. They don't do a careful balancing of the punishment versus the gains of the crime. They simply expect to get away with it.
Even if the curse is a scarier punishment than imprisonment or execution, it won't have a much greater effect. Criminals are criminals because they don't believe they'll get caught, not because they don't care if they'll be punished.
Retribution doesn't prevent criminals
The retribution aspect of punishment doesn't prevent the original crime. It prevents reprisal. And it's relatively effective when it comes to law abiding people. This punishment might feel fairer than imprisonment or even execution, but it won't do anything to prevent the original crime.
Curses won't have any effect on making the criminal better able to participate in society. They don't encourage the development of employable skills.
On the bright side, imprisonment, while better, is pretty weak on this as well. Job training programs meet the reality that most employers don't want to hire criminals. Probation programs may have the most impact, because the parole officer can demand that prisoners be self-supporting. But overall, most prisoners do not come out more employable.
Execution is of course also an utter failure at rehabilitation.
Curses don't incapacitate
As described, your curses won't keep criminals from committing more crimes. Yes, they're wearing the physical mark of the curse. But if their victims aren't able to see that because they are looking the other way or if their victims don't have anywhere to run, they can keep on committing crimes while cursed.
Imprisoned, they'd only be able to commit crimes on other prisoners or guards for the length of their incarceration.
Executed, their crime days would be over.
Incapacitation has the greatest effect on reducing crime of current punishments, and it's the aspect that loses the most. Any mild benefits from deterrence would be lost to the decline in incapacitation.
Overall, I'd expect crime to increase under this program relative to imprisonment and execution.
You could offset this by increasing the likelihood of punishment through magical means. But the fact is that this is not the optimal punishment for most of the crimes that you mention.
Murder: execution of the guilty makes sense if you can be absolutely sure who is guilty, e.g. via truth spell or divination. The two greatest arguments against are the possibility of punishing the wrong person and the idea that we're better than them. But medieval societies are unlikely to put that much weight in being better. If you absolutely insist, you can think about adding some kind of incapacitating curse on violence. But that extreme loss of self-defense capability may not be considered more just than execution.
Rape: a punishing curse for deterrence and retribution combined with an incapacitating curse like inability to get an erection.
Torture: may actually work.
Necromancy: it's unclear to me why this is on the list of the worst crimes. Maybe it would work.
I actually think that this makes more sense for lesser crimes where we use short terms of imprisonment: robbery, non-fatal violence, manslaughter, reckless endangerment, etc. The loss of the incapacitation effect has less impact and the deterrence effect on repeat offenders is more important.
In general though, the way to reduce crime is to increase the likelihood of getting caught. Someone who tries one crime and is immediately caught is much less likely to commit a second crime than someone who gets away with the first crime without consequence. And that only gets worse with the second, third, etc. crimes without consequence.
Also consider what to do with people under curses who commit new crimes. Execution? Banishment? A prison island? An incapacitating curse?