Presumably the reason is that before or during, you're doing it to stop the act. Afterwards, it's revenge.
If the punishment from the state is a slap on the wrist, it doesn’t justify retaliatory murder, but justifiable homicide when you know you’ll be raped again and perhaps killed yourself changes the calculus. No one should take matters into their own hands, but no one should be put in a position where that seems remotely appropriate.
https://www.theguardian.com/world/2020/mar/10/khachaturyan-s... | https://archive.is/L5KXZ
One man's revenge is another man's punishment.
Popular media reveals people's true preferences. People like seeing rapists killed. Because that is people's natural morality. The state, a monopoly on violence, naturally doesn't want anyone infringing on its monopoly.
Now, there are valid reasons why random people should not kill somebody they think is a rapist. Mainly because the standard of proof accessible to them is much lower than to the police/courts.
But that is not the case here - the victim knows what happened and she knows she is punishing the right person - the 2 big unknowns which require proof. Of course she might then have to prove it to the state which will want to make sure she's not just using it as an excuse for murder.
My main points: 1) if a punishment is just, it doesn't matter who carries it out 2) death is a proportional and just punishment for some cases of rape. This is a question of morality; provability is another matter.