Should violent criminals be castrated?

[Nobody]

Per your observation, that's why those who are responsible for the wrongful conviction, after that particular type of convict (wrongly so) is executed, should be held accountable.
They should be tried, and if found guilty incarcerated in a labor camp for life without parole.

Why not execute them?

Because in that one instance/case, they were caught and prosecuted for their malpractice. In the case of law enforcement and court officials, it may not be the only time. So they should see what their conduct stood to cost others subject to their authority in the event innocents were incarcerated.

Those who were executed due to their malpractice are in a coffin for eternity, so it's fitting that those responsible should be in a cell for the eternity that amounts to the rest of their life.
There is no hell, but they can at least realize what hell on earth is like for as long as they live in general population.
Civilians are always told justice keeps a civilization civil, but rarely do the authorities or the 1% ever see it when they deserve to. They buy their way out of what the poor would otherwise suffer.

That's not fair. Changing that is long over due. "Equal justice!"
Rather than what so often examples itself as a criminal system of justice.