Locking up a person, having guards to control them, having cooks to feed them, large buildings to house them, is a punishment to society and the economy. By having these people pay back society by working in fields of their choice, sounds more logical than stuffing them in a little room for specified amount of time.
If they are exiled they aren't our problem anymore. Though I don't think anyone should be forced to take that option. If another nation will take them then it should be open as an option, their citizenship revoked if they take it, and put on a "no entry" list, forbidden from ever returning.