Around 1980 Ludwig had to switch wrap suppliers and the new wraps they began using were shrinking much more than the older stuff. After a certain amount of time the wrap would pull apart along the seam. Ludwig's response was to try to secure the seam better to prevent that from happening. They decided to do so by mechanical means rather than trying a different adhesive or other production methods. The result was a low point in Ludwig history as the rivets looked bad, and didn't necessarily even work as intended (often the wrap shrank anyway creating elongated holes around each rivet).
Bill Ludwig Jr. addresses this whole incident in some detail in his autobiography. At first they were quite proud of their solution to the problem. They knew their competition was using the same wrap and assumed they would be having the same issues. They felt that they had been the first with a solution to the problem and it would give them a leg up on the other companies which were sure to have the same issue. For whatever reason the problem didn't seem to happen on Slingerland, Rogers, and Gretsch. By then Gretsch and Rogers had pretty much stopped using pearl type wraps anyhow. Slingerland still was but didn't seem to have the same issue (maybe they used better glue..?).
Anyhow after a couple of years Ludwig stopped using the rivets. Either they solved the problem another way or realized what a disaster the rivets had been. Also pearl wraps had become much less popular than natural finishes and the Cortex type solid colors.