[implements]

In the US it’s woefully abused, though - political cronies are excused their crimes as a quid pro quo in return for silence - it’s appallingly corrupt and unprincipled.

People who are guilty of a crime and prosecuted fairly under the law should generally serve their sentence. Exceptions to that are best managed by an independent and transparent tribunal who can give principled reasons for commuting specific sentences, for example a prisoner serving a very long term has undergone a genuine moral transformation and is now safe to release, or changes in society have rendered prosecutions of a certain time and place anachronistic and unjust be modern standards.

[TimTheTinker]

I'd still argue there ought to be a clemency system that is entirely outside the authority of the judicial branch.

Yes, such a system could be (and has been) abused, but given the power the judicial side has (and how that power has be abused) there has to be a system in place that checks the judicial system's power over individuals. This check prevents over-corruption in the judicial system to an extent. The point is to not allow any branch of government to gain too much power - a "separation of powers".

So many people are wrongfully convicted, either because the law is unjust (many drug laws from the 1990s, for example) or because the judicial system itself is so imperfect--from overzealous district attorneys who count their convictions as merit points (independently of the case merits) to the unjust plea bargain system to police investigators who extract false confessions.