Basically you need insulation for safety and performance. The safety issue is a no brainer. Keep the extremely high temperatures that can reach 2100 degrees away from your home and prevent a house fire.
The second reason, performance, is a more difficult one to understand for some. Here is a picture of a cap from a customer who did not use insulation around the stainless steel chimney liner. The smoke cools down too much and creates creosote. The screen was almost completely blocked on this rain cap.