Sycorax' exile is an example of the punishment going as intended. Instead of killing Sycorax and her unborn child, the people of Algiers successfully exile her to where she doesn't harm anyone else except spirits like Ariel (which they can be given a pass for not foreseeing), where she apparently dies of natural causes, and where Caliban gets to live.

And Caliban belongs on the island; his happy ending is that he's now alone on the island, free, and isn't going to hurt anyone because no one else is there. If Caliban was raised out of exile in Algiers or Milan, then his tendencies toward violence and rape would probably manifest themselves in a setting where he'd face much harsher penalties. Exile gave Caliban the best possible outcome, at least in the Tempest's universe.

(Of course Caliban is not a comfortable character to consider; he is powerless compared to Prospero and tormented by him, not to mention his resonance with post-Shakespearan anti-colonialist narratives, and these matters evoke audience sympathy. I think in the Tempest's universe, Caliban was doomed from birth to have a violent nature, no amount of kindness from Prospero or a different upbringing could have changed that, and as a result he's best on an island of his own. In the real world, Antisocial Personality Disorder is a complicated psychological issue, witches and devils aren't real, and isolation will mess up any human being.)