There is a difference between "hurting someone's feelings" and "treating them like garbage." If someone is being let go for something other than misconduct, I see no reason why they shouldn't be allowed to leave with a touch of dignity. If that means allowing them (under supervision, of course) to collect their personal effects and a few examples of their work to help them find a new job, what is the harm?
Is everyone at your company so clueless that they couldn't watch someone copy a few AI or PSD files onto a disc and still manage to stop them from destroying everything in their wake? Is your business so important to the fabric of society that you have to humiliate and degrade people who have literally changed their lives to work for you (potentially for years)?
Sad.
See coyote23's response for a more real-world-aware view.