There are only two good components in Faith being in jail anyway.
Pro prison:
1.) she turned herself in and voluntarily stayed in. A very important signal from Faith that she got it and wanted to change.
2.) prison gave her a "relative" quiet and isolated environment to come to terms with herself and her crimes since she was in no shape to just go back to slaying and protecting humanity. Similar to Willow who needed the time away in England to learn about her powers, to grief, and deal with her guilt (even though it was drastically shorten because Giles rather used her in the fight against the First, something what he never considered with Faith in S05, or after Buffy's death).
Point 2 is the most important thing, imo, and not the punishment from society (of course, for Faith, it was punishment but that's not the point).
Contra prison:
1.) the whole trial couldn't be anything else than a farce. Faith's admission of guilt still would've required circumstantial evidences, a motive, testimonies etc. which couldn't be 100 % truthful alone because of the supernatural components (not speaking of Buffy's complicity in Finch's death or the involvement of the Watcher's Council). Human law is not suitable of dealing with a case like Faith (or Willow, or Spike, or Xander, or Giles, or Angel, or Wesley, or Buffy if we're at it). She just can't have gotten a fair process. At least in my country. Please correct me if an admission of guilt suffices for a conviction in the U.S. Another problem is jurisdiction. Technically, the fight against evil is a war. Wilkins was the enemy and Faith (albeit gleefully) followed orders (assassinating Prof. Worth) from her commanding officer (as stupid as it sounds). War has its own jurisdiction so Faith should have rather brought to a court-martial, which isn't possible either because... the war is secret... a-and the Watcher's Council...it's all messed up!
2.) She's a slayer with a destiny. Her muscles, instincts and skills are way more useful for humanity (also a better way for atonement) instead of sitting behind bars and as for punishment? I think being forced by a destiny to submit herself to horrible danger and early death is punishment enough. If the Council weren't such a bunch of assholes; taking her away to a safe but confined environment, providing psychological help and sympathy and gradually building up her confidence and mind, including training, and then letting her loose again, had been the best way, especially because they already had Buffy. Yeah it's unfair to Buffy but a humane Council who helps Faith would also help Buffy with support, a salary, everything else she needs for the fight and makes her as comfortable as possible in living through her destiny.
Now to the thread subject:
Yes, Wesley was totally right (albeit the move of removing Angel's soul in the first place was incredible stupid and careless) and Giles should've considered the same instead of just deserting the cause and abandon everyone on the Hellmouth with the promise to not hang up on Dawn if she called because his precious Buffy wasn't anymore and the others, his calling, the fight, his mantra of Slayer+Hellmouth = indispensable didn't matter anymore. Faith had proven with turning herself in, voluntarily staying in, and good behavior that she's better, wants to be better and is capable to return.
Faith was needed to save Angel which, at first sight, has a slight selfish component from A.I. and Wesley's POV, but is negligible considering the voluntary and immense asset Angel represents for the cause (not speaking of the current threat of the Beast).