I'd be very surprised if any government could survive without holding secrets. Lets take something innocuous--medical records. Surely you'd have to keep those secret. And surely a foreign power would want to access those secrets as well, for blackmail if nothing else.

But even if a government tried holding no secrets, it would be at an information disadvantage compared to more secretive rivals. For instance, most people are unsatisfied with the notion of abandoning their own privacy (which is a personal form of holding secrets) as a defense against government invasions of privacy, yet this is the same solution you propose that governments attempt against rival governments.