Static is a quite legitimate issue alright! Though I often don't use a wrist strap. When you say the components are the same potential as the casing, I take it you understand we're talking about the metal casing, and that clipping yourself to the plastic case of an Amiga 500 or 1200 won't do any good at all. The amount of static present on your body is down to a wide variety of factors - the clothes you wear, the climate you live in, your shoes, the floor and desk materials, and so on. Such high voltages exist that they can easily damage components by flowing through them to ground. Strapping yourself to the casing whether it's connected to ground or not will decrease the risk of damage as you and the case are both then at the same potential, meaning very little charge can move through your parts. But really you should be grounded to a proper ground as well, whether through the mains lead of the computer or through a special grounding plug.