Yeah, it’s commonly thought to have something to do with security. Similar to chain of custody for criminal evidence.
Engineering compiles a department report for the captain. The Shift Lead puts the data on a PADD, then gives that PADD to the Chief Engineer. The Chief Engineer signs the data with their command code and notes that it is PADD-1217. That data then becomes locked to that PADD. Someone from Engineering is assigned to take PADD-1217 to the bridge and hand deliver it to the Captain. The Captain receives the PADD, reviews the report, confirms that they are holding PADD-1217, and signs the report with their command code. Someone from Engineering is sent to retrieve the PADD, and re-deliver it to the Chief Engineer. The Chief Engineer confirms the PADD was read and signed by the Captain, confirms it is PADD-1217, and transfers the signed data to the computer core to be logged and archived. The Chief Engineer then confirms all data on the PADD has been transferred and erased, then stores the PADD until it is needed again.
This is why it’s common to see a pile of PADDs on the Captain’s desk. Each department is sending their own secure report on their own PADD.