I don't necessarily disagree with you, but I can offer a third purpose for jail that I think is the most important: it keeps people who are likely to harm other

I don't necessarily disagree with you, but I can offer a third purpose for jail that I think is the most important: it keeps people who are likely to harm others from doing so. This idea is in concordance with the idea of rehabilitation (both separation and rehabilitation can happen at once), and it accommodates cases where the convicted is mentally ill.