There is no need to re register for a change of address. If you move from Escanaba to Monroe, it's all the same legally. Nobody cares. The card is also completely meaningless. You can roll it up and smoke it, file it away, or whatever else you might care to do with it. It could work well to prove it's yours in case the state police ever lost your registration information and it got stolen, but I've never even heard of that happening.
I personally threw out my little registration card years ago.