4) deterrent, to make you think twice before committing a criminal act.

The urge for long prison sentences can be explained by reasons 1, 2 and 4.

And I guess reason 3 as well; the longer someone is incarcerated, the longer they will have to think about what they did wrong and how to fix their life.

note: I don't believe that longer sentences are effective for any of those reasons, but others do